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Question 1 of 5
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Reducible equations are non-quadratic equations that can be reduced into a quadratic equation for easier solving.
First, rewrite the equation as a quadratic equation by assigning a new variable
32x-3x-72 |
= |
0 |
u2-u-72 |
= |
0 |
Substitute new variable |
Solve for u by using cross method.
u-9 |
= |
0 |
u-9 +9 |
= |
0 +9 |
u |
= |
9 |
u+8 |
= |
0 |
u+8 -8 |
= |
0 -8 |
u |
= |
-8 |
Finally, substitute u=3x to get the values of x
u |
= |
9 |
3x |
= |
9 |
Substitute u=3x |
3x |
= |
32 |
x |
= |
2 |
Equal bases means equal exponents |
u |
= |
-8 |
3x |
= |
-8 |
Substitute u=3x |
This has no solution since there is no x value that can make 3x negative
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Question 2 of 5
Solve for x
22x-3.2x-40=0
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Reducible equations are non-quadratic equations that can be reduced into a quadratic equation for easier solving.
First, rewrite the equation as a quadratic equation by assigning a new variable
22x-3.2x-40 |
= |
0 |
u2-3u-40 |
= |
0 |
Substitute new variable |
Solve for u by using cross method.
u+5 |
= |
0 |
u+5 -5 |
= |
0 -5 |
u |
= |
-5 |
u-8 |
= |
0 |
u-8 +8 |
= |
0 +8 |
u |
= |
8 |
Finally, substitute u=2x to get the values of x
u |
= |
8 |
2x |
= |
8 |
Substitute u=2x |
2x |
= |
23 |
x |
= |
3 |
Equal bases means equal exponents |
u |
= |
-5 |
2x |
= |
-5 |
Substitute u=2x |
This has no solution since there is no x value that can make 2x negative
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Question 3 of 5
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Reducible equations are non-quadratic equations that can be reduced into a quadratic equation for easier solving.
First, rewrite the equation as a quadratic equation by assigning a new variable
x4-7x2-18 |
= |
0 |
u2-7u-18 |
= |
0 |
Substitute new variable |
Solve for u by using cross method.
u-9 |
= |
0 |
u-9 +9 |
= |
0 +9 |
u |
= |
9 |
u+2 |
= |
0 |
u+2 -2 |
= |
0 -2 |
u |
= |
-2 |
Finally, substitute u=x2 to get the values of x
u |
= |
9 |
x2 |
= |
9 |
Substitute u=x2 |
√x2 |
= |
√9 |
Get the square root of both sides |
x |
= |
±3 |
u |
= |
-2 |
x2 |
= |
-2 |
Substitute u=x2 |
This has no solution since there is no x value that can make x2 negative
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Question 4 of 5
Incorrect
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Reducible equations are non-quadratic equations that can be reduced into a quadratic equation for easier solving.
First, rewrite the equation as a quadratic equation by assigning a new variable
4x4+3x2-10 |
= |
0 |
4u2+3u-10 |
= |
0 |
Substitute new variable |
Solve for u by using cross method.
4u-5 |
= |
0 |
4u-5 +5 |
= |
0 +5 |
4u |
= |
5 |
u |
= |
54 |
u+2 |
= |
0 |
u+2 -2 |
= |
0 -2 |
u |
= |
-2 |
Finally, substitute u=x2 to get the values of x
u |
= |
54 |
x2 |
= |
54 |
Substitute u=x2 |
√x2 |
= |
√54 |
Get the square root of both sides |
x |
= |
±√52 |
u |
= |
-2 |
x2 |
= |
-2 |
Substitute u=x2 |
This has no solution since there is no x value that can make x2 negative
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Question 5 of 5
Incorrect
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Reducible equations are non-quadratic equations that can be reduced into a quadratic equation for easier solving.
First, rewrite the equation as a quadratic equation by assigning a new variable
4x+3⋅2x-10 |
= |
0 |
(22)x+3⋅2x-10 |
= |
0 |
22x+3⋅2x-10 |
= |
0 |
u2+3u-10 |
= |
0 |
Substitute new variable |
Solve for u by using cross method.
u-2 |
= |
0 |
u-2 +2 |
= |
0 +2 |
u |
= |
2 |
u+5 |
= |
0 |
u+5 -5 |
= |
0 -5 |
u |
= |
-5 |
Finally, substitute u=2x to get the values of x
u |
= |
2 |
2x |
= |
2 |
Substitute u=2x |
2x |
= |
21 |
x |
= |
1 |
Equal bases means equal exponents |
u |
= |
-5 |
2x |
= |
-5 |
Substitute u=2x |
This has no solution since there is no x value that can make 3x negative