(2x+2)(x+2)=70

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Solution for (2x+2)(x+2)=70 equation: 


Simplifying
(2x + 2)(x + 2) = 70

Reorder the terms:
(2 + 2x)(x + 2) = 70

Reorder the terms:
(2 + 2x)(2 + x) = 70

Multiply (2 + 2x) * (2 + x)
(2(2 + x) + 2x * (2 + x)) = 70
((2 * 2 + x * 2) + 2x * (2 + x)) = 70
((4 + 2x) + 2x * (2 + x)) = 70
(4 + 2x + (2 * 2x + x * 2x)) = 70
(4 + 2x + (4x + 2x2)) = 70

Combine like terms: 2x + 4x = 6x
(4 + 6x + 2x2) = 70

Solving
4 + 6x + 2x2 = 70

Solving for variable 'x'.

Reorder the terms:
4 + -70 + 6x + 2x2 = 70 + -70

Combine like terms: 4 + -70 = -66
-66 + 6x + 2x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-66 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-33 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-33 + 3x + x2 = 0

Solving
-33 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + 3x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + 3x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + 3x + x2 = 0 + 33
3x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
3x + x2 = 33

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 33 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 33 + 2.25

Combine like terms: 33 + 2.25 = 35.25
2.25 + 3x + x2 = 35.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(x + 1.5) equal to 5.937171044 and -5.937171044.


Subproblem 1
x + 1.5 = 5.937171044

Simplifying
x + 1.5 = 5.937171044

Reorder the terms:
1.5 + x = 5.937171044

Solving
1.5 + x = 5.937171044

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 5.937171044 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 5.937171044 + -1.5
x = 5.937171044 + -1.5

Combine like terms: 5.937171044 + -1.5 = 4.437171044
x = 4.437171044

Simplifying
x = 4.437171044


Subproblem 2
x + 1.5 = -5.937171044

Simplifying
x + 1.5 = -5.937171044

Reorder the terms:
1.5 + x = -5.937171044

Solving
1.5 + x = -5.937171044

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -5.937171044 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -5.937171044 + -1.5
x = -5.937171044 + -1.5

Combine like terms: -5.937171044 + -1.5 = -7.437171044
x = -7.437171044

Simplifying
x = -7.437171044


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.437171044, -7.437171044}
Solution
x = {4.437171044, -7.437171044}

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