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Solving Equations Using the Quadratic Formula>
Solving Equations Using the Quadratic FormulaSolving Equations Using the Quadratic Formula
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Question 1 of 6
1. Question
Solve using the quadratic formula`x^2+2x-24=0`Hint
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Fantastic!
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The Quadratic Formula
$$x=\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$First, list the coefficients of the quadratic equation individually`x^2+2x-24=0``a=1` `b=2` `c=-24`Substitute the values into the Quadratic Formula`x` `=` $$\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$ Quadratic Formula `=` $$\frac {- \color{#9a00c7}{2} \pm \sqrt {\color{#9a00c7}{2}^2-4\color{#00880A}{(1)}\color{#007DDC}{(-24)}} }{2 \color{#00880A}{(1)}}$$ Plug in the values of `a, b` and `c` `=` $$\frac {-2 \pm \sqrt {4 +96} }{2}$$ `=` $$\frac {-2 \pm \sqrt {100} }{2}$$ `=` $$\frac {-2 \pm 10 }{2}$$ Write each root individually$$x_1$$ `=` $$\frac {-2 + 10 }{2}$$ `=` $$\frac {8}{2}$$ `=` $$4$$ $$x_2$$ `=` $$\frac {-2 – 10 }{2}$$ `=` $$\frac {-12}{2}$$ `=` $$-6$$ $$x = 4,-6$$ -
Question 2 of 6
2. Question
Solve using the quadratic formula`8x^2-8x-3=0`Hint
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The Quadratic Formula
$$x=\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$First, list the coefficients of the quadratic equation individually`8x^2-8x-3=0``a=8` `b=-8` `c=-3`Substitute the values into the Quadratic Formula`x` `=` $$\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$ Quadratic Formula `=` $$\frac {- \color{#9a00c7}{-8} \pm \sqrt {\color{#9a00c7}{-8}^2-4\color{#00880A}{(8)}\color{#007DDC}{(-3)}} }{2 \color{#00880A}{(8)}}$$ Plug in the values of `a, b` and `c` `=` $$\frac {8 \pm \sqrt {64 +96} }{16}$$ `=` $$\frac {8 \pm \sqrt {160} }{16}$$ `=` $$\frac {8 \pm 4 \sqrt{10} }{16}$$ `=` $$\frac {2 \pm \sqrt{10} }{4}$$ Simplify Write each root individually$$x_1$$ `=` $$\frac {2 + \sqrt{10} }{4}$$ `=` `1.29` $$x_2$$ `=` $$\frac {2-\sqrt{10} }{4}$$ `=` `-0.29` $$x = 1.29,-0.29$$ -
Question 3 of 6
3. Question
Solve using the quadratic formula`x^2+11x+20=0`Hint
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The Quadratic Formula
$$x=\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$First, list the coefficients of the quadratic equation individually`x^2+11x+20=0``a=1` `b=11` `c=20`Substitute the values into the Quadratic Formula`x` `=` $$\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$ Quadratic Formula `=` $$\frac {- \color{#9a00c7}{11} \pm \sqrt {\color{#9a00c7}{11}^2-4\color{#00880A}{(1)}\color{#007DDC}{(20)}} }{2 \color{#00880A}{(1)}}$$ Plug in the values of `a, b` and `c` `=` $$\frac {-11 \pm \sqrt {121 -80} }{2}$$ `=` $$\frac {-11 \pm \sqrt {41} }{2}$$ Write each root individually$$x_1$$ `=` $$\frac {-11 + \sqrt {41} }{2}$$ `=` `-2.298` $$x_2$$ `=` $$\frac {-11-\sqrt {41} }{2}$$ `=` `-8.702` $$x = -2.298,-8.702$$ -
Question 4 of 6
4. Question
Solve using the quadratic formula`-x^2-3x=-9`Hint
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The Quadratic Formula
$$x=\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$First, convert the equation to standard form`-x^2-3x` `+9` `=` `-9` `+9` `-x^2-3x+9` `=` `0` First, list the coefficients of the quadratic equation individually`-x^2-3x+9=0``a=-1` `b=-3` `c=9`Substitute the values into the Quadratic Formula`x` `=` $$\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$ Quadratic Formula `=` $$\frac {- \color{#9a00c7}{-3} \pm \sqrt {\color{#9a00c7}{-3}^2-4\color{#00880A}{(-1)}\color{#007DDC}{(9)}} }{2 \color{#00880A}{(-1)}}$$ Plug in the values of `a, b` and `c` `=` $$\frac {3 \pm \sqrt {9 +36} }{-2}$$ `=` $$\frac {3 \pm \sqrt {45} }{-2}$$ `=` $$\frac {3 \pm 3\sqrt{5} }{-2}$$ Write each root individually$$x_1$$ `=` $$\frac {3 + 3\sqrt{5} }{-2}$$ `=` `-4.854` $$x_2$$ `=` $$\frac {3-3\sqrt{5} }{-2}$$ `=` `1.854` $$x = -4.854, 1.854$$ -
Question 5 of 6
5. Question
Solve using the quadratic formula`x-3/x=4`Hint
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The Quadratic Formula
$$x=\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$First, convert the equation to standard form`x-3/x``timesx` `=` `4``timesx` `x^2-3` `-4x` `=` `4x` `-4x` `x^2-4x-3` `=` `0` First, list the coefficients of the quadratic equation individually`x^2-4x-3=0``a=1` `b=-4` `c=-3`Substitute the values into the Quadratic Formula`x` `=` $$\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$ Quadratic Formula `=` $$\frac {- \color{#9a00c7}{-4} \pm \sqrt {\color{#9a00c7}{-4}^2-4\color{#00880A}{(1)}\color{#007DDC}{(-3)}} }{2 \color{#00880A}{(1)}}$$ Plug in the values of `a, b` and `c` `=` $$\frac {4 \pm \sqrt {16+12} }{2}$$ `=` $$\frac {4 \pm \sqrt {28} }{2}$$ `=` $$\frac {4 \pm 2\sqrt{7} }{2}$$ `=` $$2 \pm \sqrt{7}$$ Simplify $$x = 2+\sqrt7, 2-\sqrt7$$ -
Question 6 of 6
6. Question
Solve using the quadratic formula`4(x+5)^2=48`Hint
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The Quadratic Formula
$$x=\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$First, write the given equation in standard form (`a``x^2+``b``x+``c`)`4(x+5)^2` `=` `48` `4(x+5)^2``-:4` `=` `48``-:4` Divide both sides by `4` `(x+5)^2` `=` `12` `x^2+10x+25` `=` `12` `x^2+10x+25``-12` `=` `12``-12` Subtract `12` from both sides `x^2+10x+13` `=` `0` Next, list the coefficients of the quadratic equation individually`x^2+10x+13=0``a=1` `b=10` `c=13`Substitute the values into the Quadratic Formula`x` `=` $$\frac {-\color{#9a00c7}{b} \pm \sqrt {\color{#9a00c7}{b}^2-4\color{#00880A}{a}\color{#007DDC}{c}} }{2 \color{#00880A}{a}}$$ Quadratic Formula `=` $$\frac {- \color{#9a00c7}{10} \pm \sqrt {\color{#9a00c7}{10}^2-4\color{#00880A}{(1)}\color{#007DDC}{(13)}} }{2 \color{#00880A}{(1)}}$$ Plug in the values of `a, b` and `c` `=` $$\frac {-10 \pm \sqrt {100 -52} }{2}$$ `=` $$\frac {-10 \pm \sqrt {48} }{2}$$ `=` $$\frac {-10 \pm 4\sqrt3 }{2}$$ `=` $$-5 \pm 2\sqrt3$$ The roots can also be written individually`=` $$-5+2\sqrt3$$ `=` $$-5- 2\sqrt3$$ $$x = -5 \pm 2\sqrt3$$
Quizzes
- Sum & Product of Roots 1
- Sum & Product of Roots 2
- Sum & Product of Roots 3
- Sum & Product of Roots 4
- Solving Equations by Factoring 1
- Solving Equations Using the Quadratic Formula
- Completing the Square 1
- Completing the Square 2
- Intro to Quadratic Functions (Parabolas) 1
- Intro to Quadratic Functions (Parabolas) 2
- Intro to Quadratic Functions (Parabolas) 3
- Graph Quadratic Functions in Standard Form 1
- Graph Quadratic Functions in Standard Form 2
- Graph Quadratic Functions by Completing the Square
- Graph Quadratic Functions in Vertex Form
- Write a Quadratic Equation from the Graph
- Write a Quadratic Equation Given the Vertex and Another Point
- Quadratic Inequalities 1
- Quadratic Inequalities 2
- Quadratics Word Problems 1
- Quadratics Word Problems 2
- Quadratic Identities
- Graphing Quadratics Using the Discriminant
- Positive and Negative Definite
- Applications of the Discriminant 1
- Applications of the Discriminant 2
- Solving Reducible Equations