(x+2)(x+2)=8+x

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Solution for (x+2)(x+2)=8+x equation:


Simplifying
(x + 2)(x + 2) = 8 + x

Reorder the terms:
(2 + x)(x + 2) = 8 + x

Reorder the terms:
(2 + x)(2 + x) = 8 + x

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x)) = 8 + x
((2 * 2 + x * 2) + x(2 + x)) = 8 + x
((4 + 2x) + x(2 + x)) = 8 + x
(4 + 2x + (2 * x + x * x)) = 8 + x
(4 + 2x + (2x + x2)) = 8 + x

Combine like terms: 2x + 2x = 4x
(4 + 4x + x2) = 8 + x

Solving
4 + 4x + x2 = 8 + x

Solving for variable 'x'.

Reorder the terms:
4 + -8 + 4x + -1x + x2 = 8 + x + -8 + -1x

Combine like terms: 4 + -8 = -4
-4 + 4x + -1x + x2 = 8 + x + -8 + -1x

Combine like terms: 4x + -1x = 3x
-4 + 3x + x2 = 8 + x + -8 + -1x

Reorder the terms:
-4 + 3x + x2 = 8 + -8 + x + -1x

Combine like terms: 8 + -8 = 0
-4 + 3x + x2 = 0 + x + -1x
-4 + 3x + x2 = x + -1x

Combine like terms: x + -1x = 0
-4 + 3x + x2 = 0

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

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 '(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

Solution

x = {-4, 1}

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