2x^2-10=8x

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Solution for 2x^2-10=8x equation:


Simplifying
2x2 + -10 = 8x

Reorder the terms:
-10 + 2x2 = 8x

Solving
-10 + 2x2 = 8x

Solving for variable 'x'.

Reorder the terms:
-10 + -8x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-10 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1

Subproblem 2

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

Solution

x = {-1, 5}

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