x^2+14x-159=0

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Solution for x^2+14x-159=0 equation:


Simplifying
x2 + 14x + -159 = 0

Reorder the terms:
-159 + 14x + x2 = 0

Solving
-159 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '159' to each side of the equation.
-159 + 14x + 159 + x2 = 0 + 159

Reorder the terms:
-159 + 159 + 14x + x2 = 0 + 159

Combine like terms: -159 + 159 = 0
0 + 14x + x2 = 0 + 159
14x + x2 = 0 + 159

Combine like terms: 0 + 159 = 159
14x + x2 = 159

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 = 159 + 49

Reorder the terms:
49 + 14x + x2 = 159 + 49

Combine like terms: 159 + 49 = 208
49 + 14x + x2 = 208

Factor a perfect square on the left side:
(x + 7)(x + 7) = 208

Calculate the square root of the right side: 14.422205102

Break this problem into two subproblems by setting 
(x + 7) equal to 14.422205102 and -14.422205102.


Subproblem 1
x + 7 = 14.422205102

Simplifying
x + 7 = 14.422205102

Reorder the terms:
7 + x = 14.422205102

Solving
7 + x = 14.422205102

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 = 14.422205102 + -7

Combine like terms: 7 + -7 = 0
0 + x = 14.422205102 + -7
x = 14.422205102 + -7

Combine like terms: 14.422205102 + -7 = 7.422205102
x = 7.422205102

Simplifying
x = 7.422205102


Subproblem 2
x + 7 = -14.422205102

Simplifying
x + 7 = -14.422205102

Reorder the terms:
7 + x = -14.422205102

Solving
7 + x = -14.422205102

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 = -14.422205102 + -7

Combine like terms: 7 + -7 = 0
0 + x = -14.422205102 + -7
x = -14.422205102 + -7

Combine like terms: -14.422205102 + -7 = -21.422205102
x = -21.422205102

Simplifying
x = -21.422205102


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.422205102, -21.422205102}

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