4x^2+4x-152=0

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Solution for 4x^2+4x-152=0 equation: 


Simplifying
4x2 + 4x + -152 = 0

Reorder the terms:
-152 + 4x + 4x2 = 0

Solving
-152 + 4x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-38 + x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-38 + x + x2)' equal to zero and attempt to solve:

Simplifying
-38 + x + x2 = 0

Solving
-38 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + x + x2 = 0 + 38
x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
x + x2 = 38

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 38 + 0.25

Reorder the terms:
0.25 + x + x2 = 38 + 0.25

Combine like terms: 38 + 0.25 = 38.25
0.25 + x + x2 = 38.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
x + 0.5 = 6.184658438

Simplifying
x + 0.5 = 6.184658438

Reorder the terms:
0.5 + x = 6.184658438

Solving
0.5 + x = 6.184658438

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 6.184658438 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 6.184658438 + -0.5
x = 6.184658438 + -0.5

Combine like terms: 6.184658438 + -0.5 = 5.684658438
x = 5.684658438

Simplifying
x = 5.684658438


Subproblem 2
x + 0.5 = -6.184658438

Simplifying
x + 0.5 = -6.184658438

Reorder the terms:
0.5 + x = -6.184658438

Solving
0.5 + x = -6.184658438

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -6.184658438 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -6.184658438 + -0.5
x = -6.184658438 + -0.5

Combine like terms: -6.184658438 + -0.5 = -6.684658438
x = -6.684658438

Simplifying
x = -6.684658438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.684658438, -6.684658438}
Solution
x = {5.684658438, -6.684658438}

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