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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 formulax2+2x-24=0- 1.
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The Quadratic Formula
x=−b±√b2−4ac2aFirst, list the coefficients of the quadratic equation individuallyx2+2x-24=0a=1 b=2 c=-24Substitute the values into the Quadratic Formulax = −b±√b2−4ac2a Quadratic Formula = −2±√22−4(1)(−24)2(1) Plug in the values of a,b and c = −2±√4+962 = −2±√1002 = −2±102 Write each root individuallyx1 = −2+102 = 82 = 4 x2 = −2–102 = −122 = −6 x=4,−6 -
Question 2 of 6
2. Question
Solve using the quadratic formula8x2-8x-3=0-
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The Quadratic Formula
x=−b±√b2−4ac2aFirst, list the coefficients of the quadratic equation individually8x2-8x-3=0a=8 b=-8 c=-3Substitute the values into the Quadratic Formulax = −b±√b2−4ac2a Quadratic Formula = −−8±√−82−4(8)(−3)2(8) Plug in the values of a,b and c = 8±√64+9616 = 8±√16016 = 8±4√1016 = 2±√104 Simplify Write each root individuallyx1 = 2+√104 = 1.29 x2 = 2−√104 = -0.29 x=1.29,−0.29 -
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Question 3 of 6
3. Question
Solve using the quadratic formulax2+11x+20=0-
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The Quadratic Formula
x=−b±√b2−4ac2aFirst, list the coefficients of the quadratic equation individuallyx2+11x+20=0a=1 b=11 c=20Substitute the values into the Quadratic Formulax = −b±√b2−4ac2a Quadratic Formula = −11±√112−4(1)(20)2(1) Plug in the values of a,b and c = −11±√121−802 = −11±√412 Write each root individuallyx1 = −11+√412 = -2.298 x2 = −11−√412 = -8.702 x=−2.298,−8.702 -
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Question 4 of 6
4. Question
Solve using the quadratic formula-x2-3x=-9-
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Chapters- Chapters
The Quadratic Formula
x=−b±√b2−4ac2aFirst, convert the equation to standard form-x2-3x +9 = -9 +9 -x2-3x+9 = 0 First, list the coefficients of the quadratic equation individually-x2-3x+9=0a=-1 b=-3 c=9Substitute the values into the Quadratic Formulax = −b±√b2−4ac2a Quadratic Formula = −−3±√−32−4(−1)(9)2(−1) Plug in the values of a,b and c = 3±√9+36−2 = 3±√45−2 = 3±3√5−2 Write each root individuallyx1 = 3+3√5−2 = -4.854 x2 = 3−3√5−2 = 1.854 x=−4.854,1.854 -
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Question 5 of 6
5. Question
Solve using the quadratic formulax-3x=4-
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Chapters- Chapters
The Quadratic Formula
x=−b±√b2−4ac2aFirst, convert the equation to standard formx-3x×x = 4×x x2-3 -4x = 4x -4x x2-4x-3 = 0 First, list the coefficients of the quadratic equation individuallyx2-4x-3=0a=1 b=-4 c=-3Substitute the values into the Quadratic Formulax = −b±√b2−4ac2a Quadratic Formula = −−4±√−42−4(1)(−3)2(1) Plug in the values of a,b and c = 4±√16+122 = 4±√282 = 4±2√72 = 2±√7 Simplify x=2+√7,2−√7 -
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Question 6 of 6
6. Question
Solve using the quadratic formula4(x+5)2=48-
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Chapters- Chapters
The Quadratic Formula
x=−b±√b2−4ac2aFirst, write the given equation in standard form (ax2+bx+c)4(x+5)2 = 48 4(x+5)2÷4 = 48÷4 Divide both sides by 4 (x+5)2 = 12 x2+10x+25 = 12 x2+10x+25-12 = 12-12 Subtract 12 from both sides x2+10x+13 = 0 Next, list the coefficients of the quadratic equation individuallyx2+10x+13=0a=1 b=10 c=13Substitute the values into the Quadratic Formulax = −b±√b2−4ac2a Quadratic Formula = −10±√102−4(1)(13)2(1) Plug in the values of a,b and c = −10±√100−522 = −10±√482 = −10±4√32 = −5±2√3 The roots can also be written individually= −5+2√3 = −5−2√3 x=−5±2√3 -
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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