4(x+2)(x+2)+5=10

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Solution for 4(x+2)(x+2)+5=10 equation: 


Simplifying
4(x + 2)(x + 2) + 5 = 10

Reorder the terms:
4(2 + x)(x + 2) + 5 = 10

Reorder the terms:
4(2 + x)(2 + x) + 5 = 10

Multiply (2 + x) * (2 + x)
4(2(2 + x) + x(2 + x)) + 5 = 10
4((2 * 2 + x * 2) + x(2 + x)) + 5 = 10
4((4 + 2x) + x(2 + x)) + 5 = 10
4(4 + 2x + (2 * x + x * x)) + 5 = 10
4(4 + 2x + (2x + x2)) + 5 = 10

Combine like terms: 2x + 2x = 4x
4(4 + 4x + x2) + 5 = 10
(4 * 4 + 4x * 4 + x2 * 4) + 5 = 10
(16 + 16x + 4x2) + 5 = 10

Reorder the terms:
16 + 5 + 16x + 4x2 = 10

Combine like terms: 16 + 5 = 21
21 + 16x + 4x2 = 10

Solving
21 + 16x + 4x2 = 10

Solving for variable 'x'.

Reorder the terms:
21 + -10 + 16x + 4x2 = 10 + -10

Combine like terms: 21 + -10 = 11
11 + 16x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
11 + 16x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
2.75 + 4x + x2 = 0

Move the constant term to the right:

Add '-2.75' to each side of the equation.
2.75 + 4x + -2.75 + x2 = 0 + -2.75

Reorder the terms:
2.75 + -2.75 + 4x + x2 = 0 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + 4x + x2 = 0 + -2.75
4x + x2 = 0 + -2.75

Combine like terms: 0 + -2.75 = -2.75
4x + x2 = -2.75

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -2.75 + 4

Reorder the terms:
4 + 4x + x2 = -2.75 + 4

Combine like terms: -2.75 + 4 = 1.25
4 + 4x + x2 = 1.25

Factor a perfect square on the left side:
(x + 2)(x + 2) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 2) equal to 1.118033989 and -1.118033989.


Subproblem 1
x + 2 = 1.118033989

Simplifying
x + 2 = 1.118033989

Reorder the terms:
2 + x = 1.118033989

Solving
2 + x = 1.118033989

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 1.118033989 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.118033989 + -2
x = 1.118033989 + -2

Combine like terms: 1.118033989 + -2 = -0.881966011
x = -0.881966011

Simplifying
x = -0.881966011


Subproblem 2
x + 2 = -1.118033989

Simplifying
x + 2 = -1.118033989

Reorder the terms:
2 + x = -1.118033989

Solving
2 + x = -1.118033989

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = -1.118033989 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.118033989 + -2
x = -1.118033989 + -2

Combine like terms: -1.118033989 + -2 = -3.118033989
x = -3.118033989

Simplifying
x = -3.118033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.881966011, -3.118033989}

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