x^2+14x-52=0

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Solution for x^2+14x-52=0 equation: 


Simplifying
x2 + 14x + -52 = 0

Reorder the terms:
-52 + 14x + x2 = 0

Solving
-52 + 14x + 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 + 14x + 52 + x2 = 0 + 52

Reorder the terms:
-52 + 52 + 14x + x2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + 14x + x2 = 0 + 52
14x + x2 = 0 + 52

Combine like terms: 0 + 52 = 52
14x + x2 = 52

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 52 + 49

Reorder the terms:
49 + 14x + x2 = 52 + 49

Combine like terms: 52 + 49 = 101
49 + 14x + x2 = 101

Factor a perfect square on the left side:
(x + 7)(x + 7) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(x + 7) equal to 10.049875621 and -10.049875621.


Subproblem 1
x + 7 = 10.049875621

Simplifying
x + 7 = 10.049875621

Reorder the terms:
7 + x = 10.049875621

Solving
7 + x = 10.049875621

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 10.049875621 + -7

Combine like terms: 7 + -7 = 0
0 + x = 10.049875621 + -7
x = 10.049875621 + -7

Combine like terms: 10.049875621 + -7 = 3.049875621
x = 3.049875621

Simplifying
x = 3.049875621


Subproblem 2
x + 7 = -10.049875621

Simplifying
x + 7 = -10.049875621

Reorder the terms:
7 + x = -10.049875621

Solving
7 + x = -10.049875621

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -10.049875621 + -7

Combine like terms: 7 + -7 = 0
0 + x = -10.049875621 + -7
x = -10.049875621 + -7

Combine like terms: -10.049875621 + -7 = -17.049875621
x = -17.049875621

Simplifying
x = -17.049875621


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.049875621, -17.049875621}

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