4(x-7)(x-7)=64

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Solution for 4(x-7)(x-7)=64 equation:


Simplifying
4(x + -7)(x + -7) = 64

Reorder the terms:
4(-7 + x)(x + -7) = 64

Reorder the terms:
4(-7 + x)(-7 + x) = 64

Multiply (-7 + x) * (-7 + x)
4(-7(-7 + x) + x(-7 + x)) = 64
4((-7 * -7 + x * -7) + x(-7 + x)) = 64
4((49 + -7x) + x(-7 + x)) = 64
4(49 + -7x + (-7 * x + x * x)) = 64
4(49 + -7x + (-7x + x2)) = 64

Combine like terms: -7x + -7x = -14x
4(49 + -14x + x2) = 64
(49 * 4 + -14x * 4 + x2 * 4) = 64
(196 + -56x + 4x2) = 64

Solving
196 + -56x + 4x2 = 64

Solving for variable 'x'.

Reorder the terms:
196 + -64 + -56x + 4x2 = 64 + -64

Combine like terms: 196 + -64 = 132
132 + -56x + 4x2 = 64 + -64

Combine like terms: 64 + -64 = 0
132 + -56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(33 + -14x + x2) = 0

Factor a trinomial.
4((3 + -1x)(11 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11

Solution

x = {3, 11}

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