x^2+4x-52=0

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


Simplifying
x2 + 4x + -52 = 0

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

Solving
-52 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + 4x + 52 + x2 = 0 + 52

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

Combine like terms: -52 + 52 = 0
0 + 4x + x2 = 0 + 52
4x + x2 = 0 + 52

Combine like terms: 0 + 52 = 52
4x + x2 = 52

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 52 + 4

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

Combine like terms: 52 + 4 = 56
4 + 4x + x2 = 56

Factor a perfect square on the left side:
(x + 2)(x + 2) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + 2) equal to 7.483314774 and -7.483314774.


Subproblem 1
x + 2 = 7.483314774

Simplifying
x + 2 = 7.483314774

Reorder the terms:
2 + x = 7.483314774

Solving
2 + x = 7.483314774

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 7.483314774 + -2

Combine like terms: 2 + -2 = 0
0 + x = 7.483314774 + -2
x = 7.483314774 + -2

Combine like terms: 7.483314774 + -2 = 5.483314774
x = 5.483314774

Simplifying
x = 5.483314774


Subproblem 2
x + 2 = -7.483314774

Simplifying
x + 2 = -7.483314774

Reorder the terms:
2 + x = -7.483314774

Solving
2 + x = -7.483314774

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -7.483314774 + -2

Combine like terms: 2 + -2 = 0
0 + x = -7.483314774 + -2
x = -7.483314774 + -2

Combine like terms: -7.483314774 + -2 = -9.483314774
x = -9.483314774

Simplifying
x = -9.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.483314774, -9.483314774}

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