(x+4)(x+4)=10

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Solution for (x+4)(x+4)=10 equation: 


Simplifying
(x + 4)(x + 4) = 10

Reorder the terms:
(4 + x)(x + 4) = 10

Reorder the terms:
(4 + x)(4 + x) = 10

Multiply (4 + x) * (4 + x)
(4(4 + x) + x(4 + x)) = 10
((4 * 4 + x * 4) + x(4 + x)) = 10
((16 + 4x) + x(4 + x)) = 10
(16 + 4x + (4 * x + x * x)) = 10
(16 + 4x + (4x + x2)) = 10

Combine like terms: 4x + 4x = 8x
(16 + 8x + x2) = 10

Solving
16 + 8x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
16 + -10 + 8x + x2 = 10 + -10

Combine like terms: 16 + -10 = 6
6 + 8x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
6 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 8x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 8x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 8x + x2 = 0 + -6
8x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
8x + x2 = -6

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 = -6 + 16

Reorder the terms:
16 + 8x + x2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + 8x + x2 = 10

Factor a perfect square on the left side:
(x + 4)(x + 4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 4) equal to 3.16227766 and -3.16227766.


Subproblem 1
x + 4 = 3.16227766

Simplifying
x + 4 = 3.16227766

Reorder the terms:
4 + x = 3.16227766

Solving
4 + x = 3.16227766

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 = 3.16227766 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.16227766 + -4
x = 3.16227766 + -4

Combine like terms: 3.16227766 + -4 = -0.83772234
x = -0.83772234

Simplifying
x = -0.83772234


Subproblem 2
x + 4 = -3.16227766

Simplifying
x + 4 = -3.16227766

Reorder the terms:
4 + x = -3.16227766

Solving
4 + x = -3.16227766

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 = -3.16227766 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.16227766 + -4
x = -3.16227766 + -4

Combine like terms: -3.16227766 + -4 = -7.16227766
x = -7.16227766

Simplifying
x = -7.16227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.83772234, -7.16227766}

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