MATH SOLVE

7 months ago

Q:
# Which of the following are solutions to 2x^2-8x-90? select all that apply.

Accepted Solution

A:

Simplifying:

2x2 + -8x + -90 = 0

Reorder the terms:

-90 + -8x + 2x2 = 0

Solving

-90 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.

2(-45 + -4x + x2) = 0

Factor a trinomial.

2((-5 + -1x)(9 + -1x)) = 0

Ignore the factor 2.

Subproblem 1:

Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying

-5 + -1x = 0

Solving

-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.

-5 + 5 + -1x = 0 + 5

Combine like terms:

-5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5

Combine like terms:

0 + 5 = 5 -1x = 5

Divide each side by '-1'.

x = -5

Simplifying

x = -5

Subproblem 2:

Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying

9 + -1x = 0

Solving

9 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.

9 + -9 + -1x = 0 + -9

Combine like terms:

9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9

Combine like terms:

0 + -9 = -9 -1x = -9

Divide each side by '-1'.

x = 9

Simplifying x = 9

Solution

x = {-5, 9}

2x2 + -8x + -90 = 0

Reorder the terms:

-90 + -8x + 2x2 = 0

Solving

-90 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.

2(-45 + -4x + x2) = 0

Factor a trinomial.

2((-5 + -1x)(9 + -1x)) = 0

Ignore the factor 2.

Subproblem 1:

Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying

-5 + -1x = 0

Solving

-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.

-5 + 5 + -1x = 0 + 5

Combine like terms:

-5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5

Combine like terms:

0 + 5 = 5 -1x = 5

Divide each side by '-1'.

x = -5

Simplifying

x = -5

Subproblem 2:

Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying

9 + -1x = 0

Solving

9 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.

9 + -9 + -1x = 0 + -9

Combine like terms:

9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9

Combine like terms:

0 + -9 = -9 -1x = -9

Divide each side by '-1'.

x = 9

Simplifying x = 9

Solution

x = {-5, 9}