x^2+16x=32x-64

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Solution for x^2+16x=32x-64 equation:


Simplifying
x2 + 16x = 32x + -64

Reorder the terms:
16x + x2 = 32x + -64

Reorder the terms:
16x + x2 = -64 + 32x

Solving
16x + x2 = -64 + 32x

Solving for variable 'x'.

Reorder the terms:
64 + 16x + -32x + x2 = -64 + 32x + 64 + -32x

Combine like terms: 16x + -32x = -16x
64 + -16x + x2 = -64 + 32x + 64 + -32x

Reorder the terms:
64 + -16x + x2 = -64 + 64 + 32x + -32x

Combine like terms: -64 + 64 = 0
64 + -16x + x2 = 0 + 32x + -32x
64 + -16x + x2 = 32x + -32x

Combine like terms: 32x + -32x = 0
64 + -16x + x2 = 0

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

Subproblem 1

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

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 = {8, 8}

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