x^2+7x-52=0

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Solution for x^2+7x-52=0 equation: 


Simplifying
x2 + 7x + -52 = 0

Reorder the terms:
-52 + 7x + x2 = 0

Solving
-52 + 7x + 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 + 7x + 52 + x2 = 0 + 52

Reorder the terms:
-52 + 52 + 7x + x2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + 7x + x2 = 0 + 52
7x + x2 = 0 + 52

Combine like terms: 0 + 52 = 52
7x + x2 = 52

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 = 52 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 52 + 12.25

Combine like terms: 52 + 12.25 = 64.25
12.25 + 7x + x2 = 64.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(x + 3.5) equal to 8.015609771 and -8.015609771.


Subproblem 1
x + 3.5 = 8.015609771

Simplifying
x + 3.5 = 8.015609771

Reorder the terms:
3.5 + x = 8.015609771

Solving
3.5 + x = 8.015609771

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 = 8.015609771 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 8.015609771 + -3.5
x = 8.015609771 + -3.5

Combine like terms: 8.015609771 + -3.5 = 4.515609771
x = 4.515609771

Simplifying
x = 4.515609771


Subproblem 2
x + 3.5 = -8.015609771

Simplifying
x + 3.5 = -8.015609771

Reorder the terms:
3.5 + x = -8.015609771

Solving
3.5 + x = -8.015609771

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 = -8.015609771 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -8.015609771 + -3.5
x = -8.015609771 + -3.5

Combine like terms: -8.015609771 + -3.5 = -11.515609771
x = -11.515609771

Simplifying
x = -11.515609771


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.515609771, -11.515609771}

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