x^2=10x-16

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Solution for x^2=10x-16 equation:


Simplifying
x2 = 10x + -16

Reorder the terms:
x2 = -16 + 10x

Solving
x2 = -16 + 10x

Solving for variable 'x'.

Reorder the terms:
16 + -10x + x2 = -16 + 10x + 16 + -10x

Reorder the terms:
16 + -10x + x2 = -16 + 16 + 10x + -10x

Combine like terms: -16 + 16 = 0
16 + -10x + x2 = 0 + 10x + -10x
16 + -10x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
16 + -10x + x2 = 0

Factor a trinomial.
(2 + -1x)(8 + -1x) = 0

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {2, 8}

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