x*x-14x-52=

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Solution for x*x-14x-52= equation: 


Simplifying
x * x + -14x + -52 = 0

Multiply x * x
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 = 17.049875621
x = 17.049875621

Simplifying
x = 17.049875621


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 = -3.049875621
x = -3.049875621

Simplifying
x = -3.049875621


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

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