(x+4)(x+4)=8

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Solution for (x+4)(x+4)=8 equation:


Simplifying
(x + 4)(x + 4) = 8

Reorder the terms:
(4 + x)(x + 4) = 8

Reorder the terms:
(4 + x)(4 + x) = 8

Multiply (4 + x) * (4 + x)
(4(4 + x) + x(4 + x)) = 8
((4 * 4 + x * 4) + x(4 + x)) = 8
((16 + 4x) + x(4 + x)) = 8
(16 + 4x + (4 * x + x * x)) = 8
(16 + 4x + (4x + x2)) = 8

Combine like terms: 4x + 4x = 8x
(16 + 8x + x2) = 8

Solving
16 + 8x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
16 + -8 + 8x + x2 = 8 + -8

Combine like terms: 16 + -8 = 8
8 + 8x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
8 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 8x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 8x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 8x + x2 = 0 + -8
8x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
8x + x2 = -8

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -8 + 16

Reorder the terms:
16 + 8x + x2 = -8 + 16

Combine like terms: -8 + 16 = 8
16 + 8x + x2 = 8

Factor a perfect square on the left side:
(x + 4)(x + 4) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 4) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + 4 = 2.828427125 Simplifying x + 4 = 2.828427125 Reorder the terms: 4 + x = 2.828427125 Solving 4 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 2.828427125 + -4 Combine like terms: 4 + -4 = 0 0 + x = 2.828427125 + -4 x = 2.828427125 + -4 Combine like terms: 2.828427125 + -4 = -1.171572875 x = -1.171572875 Simplifying x = -1.171572875

Subproblem 2

x + 4 = -2.828427125 Simplifying x + 4 = -2.828427125 Reorder the terms: 4 + x = -2.828427125 Solving 4 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -2.828427125 + -4 Combine like terms: 4 + -4 = 0 0 + x = -2.828427125 + -4 x = -2.828427125 + -4 Combine like terms: -2.828427125 + -4 = -6.828427125 x = -6.828427125 Simplifying x = -6.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.171572875, -6.828427125}

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