2x^2=8x+90

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Solution for 2x^2=8x+90 equation:


Simplifying
2x2 = 8x + 90

Reorder the terms:
2x2 = 90 + 8x

Solving
2x2 = 90 + 8x

Solving for variable 'x'.

Reorder the terms:
-90 + -8x + 2x2 = 90 + 8x + -90 + -8x

Reorder the terms:
-90 + -8x + 2x2 = 90 + -90 + 8x + -8x

Combine like terms: 90 + -90 = 0
-90 + -8x + 2x2 = 0 + 8x + -8x
-90 + -8x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-90 + -8x + 2x2 = 0

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}

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