4x^2+4x-52=0

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Solution for 4x^2+4x-52=0 equation: 


Simplifying
4x2 + 4x + -52 = 0

Reorder the terms:
-52 + 4x + 4x2 = 0

Solving
-52 + 4x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-13 + x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-13 + x + x2)' equal to zero and attempt to solve:

Simplifying
-13 + x + x2 = 0

Solving
-13 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + x + x2 = 0 + 13
x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
x + x2 = 13

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 = 13 + 0.25

Reorder the terms:
0.25 + x + x2 = 13 + 0.25

Combine like terms: 13 + 0.25 = 13.25
0.25 + x + x2 = 13.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
x + 0.5 = 3.640054945

Simplifying
x + 0.5 = 3.640054945

Reorder the terms:
0.5 + x = 3.640054945

Solving
0.5 + x = 3.640054945

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 = 3.640054945 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.640054945 + -0.5
x = 3.640054945 + -0.5

Combine like terms: 3.640054945 + -0.5 = 3.140054945
x = 3.140054945

Simplifying
x = 3.140054945


Subproblem 2
x + 0.5 = -3.640054945

Simplifying
x + 0.5 = -3.640054945

Reorder the terms:
0.5 + x = -3.640054945

Solving
0.5 + x = -3.640054945

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 = -3.640054945 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.640054945 + -0.5
x = -3.640054945 + -0.5

Combine like terms: -3.640054945 + -0.5 = -4.140054945
x = -4.140054945

Simplifying
x = -4.140054945


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.140054945, -4.140054945}
Solution
x = {3.140054945, -4.140054945}

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