(2x+2)(2x+7)=10

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Solution for (2x+2)(2x+7)=10 equation: 


Simplifying
(2x + 2)(2x + 7) = 10

Reorder the terms:
(2 + 2x)(2x + 7) = 10

Reorder the terms:
(2 + 2x)(7 + 2x) = 10

Multiply (2 + 2x) * (7 + 2x)
(2(7 + 2x) + 2x * (7 + 2x)) = 10
((7 * 2 + 2x * 2) + 2x * (7 + 2x)) = 10
((14 + 4x) + 2x * (7 + 2x)) = 10
(14 + 4x + (7 * 2x + 2x * 2x)) = 10
(14 + 4x + (14x + 4x2)) = 10

Combine like terms: 4x + 14x = 18x
(14 + 18x + 4x2) = 10

Solving
14 + 18x + 4x2 = 10

Solving for variable 'x'.

Reorder the terms:
14 + -10 + 18x + 4x2 = 10 + -10

Combine like terms: 14 + -10 = 4
4 + 18x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
4 + 18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 9x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + 9x + 2x2)' equal to zero and attempt to solve:

Simplifying
2 + 9x + 2x2 = 0

Solving
2 + 9x + 2x2 = 0

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

Divide each side by '2'.
1 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 4.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4.5x + x2 = 0 + -1
4.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
4.5x + x2 = -1

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -1 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -1 + 5.0625

Combine like terms: -1 + 5.0625 = 4.0625
5.0625 + 4.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.015564437 and -2.015564437.


Subproblem 1
x + 2.25 = 2.015564437

Simplifying
x + 2.25 = 2.015564437

Reorder the terms:
2.25 + x = 2.015564437

Solving
2.25 + x = 2.015564437

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 2.015564437 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.015564437 + -2.25
x = 2.015564437 + -2.25

Combine like terms: 2.015564437 + -2.25 = -0.234435563
x = -0.234435563

Simplifying
x = -0.234435563


Subproblem 2
x + 2.25 = -2.015564437

Simplifying
x + 2.25 = -2.015564437

Reorder the terms:
2.25 + x = -2.015564437

Solving
2.25 + x = -2.015564437

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -2.015564437 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.015564437 + -2.25
x = -2.015564437 + -2.25

Combine like terms: -2.015564437 + -2.25 = -4.265564437
x = -4.265564437

Simplifying
x = -4.265564437


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.234435563, -4.265564437}
Solution
x = {-0.234435563, -4.265564437}

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