2(x^2+7x-141)=0

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Solution for 2(x^2+7x-141)=0 equation: 


Simplifying
2(x2 + 7x + -141) = 0

Reorder the terms:
2(-141 + 7x + x2) = 0
(-141 * 2 + 7x * 2 + x2 * 2) = 0
(-282 + 14x + 2x2) = 0

Solving
-282 + 14x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-141 + 7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-141 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-141 + 7x + x2 = 0

Solving
-141 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '141' to each side of the equation.
-141 + 7x + 141 + x2 = 0 + 141

Reorder the terms:
-141 + 141 + 7x + x2 = 0 + 141

Combine like terms: -141 + 141 = 0
0 + 7x + x2 = 0 + 141
7x + x2 = 0 + 141

Combine like terms: 0 + 141 = 141
7x + x2 = 141

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 141 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 141 + 12.25

Combine like terms: 141 + 12.25 = 153.25
12.25 + 7x + x2 = 153.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 153.25

Calculate the square root of the right side: 12.379418403

Break this problem into two subproblems by setting 
(x + 3.5) equal to 12.379418403 and -12.379418403.


Subproblem 1
x + 3.5 = 12.379418403

Simplifying
x + 3.5 = 12.379418403

Reorder the terms:
3.5 + x = 12.379418403

Solving
3.5 + x = 12.379418403

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 12.379418403 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 12.379418403 + -3.5
x = 12.379418403 + -3.5

Combine like terms: 12.379418403 + -3.5 = 8.879418403
x = 8.879418403

Simplifying
x = 8.879418403


Subproblem 2
x + 3.5 = -12.379418403

Simplifying
x + 3.5 = -12.379418403

Reorder the terms:
3.5 + x = -12.379418403

Solving
3.5 + x = -12.379418403

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -12.379418403 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -12.379418403 + -3.5
x = -12.379418403 + -3.5

Combine like terms: -12.379418403 + -3.5 = -15.879418403
x = -15.879418403

Simplifying
x = -15.879418403


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.879418403, -15.879418403}
Solution
x = {8.879418403, -15.879418403}

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