4x^2=32x-64

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Solution for 4x^2=32x-64 equation:


Simplifying
4x2 = 32x + -64

Reorder the terms:
4x2 = -64 + 32x

Solving
4x2 = -64 + 32x

Solving for variable 'x'.

Reorder the terms:
64 + -32x + 4x2 = -64 + 32x + 64 + -32x

Reorder the terms:
64 + -32x + 4x2 = -64 + 64 + 32x + -32x

Combine like terms: -64 + 64 = 0
64 + -32x + 4x2 = 0 + 32x + -32x
64 + -32x + 4x2 = 32x + -32x

Combine like terms: 32x + -32x = 0
64 + -32x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + -8x + x2) = 0

Factor a trinomial.
4((4 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {4, 4}

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