x^2+14x-9=0

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Solution for x^2+14x-9=0 equation: 


Simplifying
x2 + 14x + -9 = 0

Reorder the terms:
-9 + 14x + x2 = 0

Solving
-9 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 14x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 14x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 14x + x2 = 0 + 9
14x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
14x + x2 = 9

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 = 9 + 49

Reorder the terms:
49 + 14x + x2 = 9 + 49

Combine like terms: 9 + 49 = 58
49 + 14x + x2 = 58

Factor a perfect square on the left side:
(x + 7)(x + 7) = 58

Calculate the square root of the right side: 7.615773106

Break this problem into two subproblems by setting 
(x + 7) equal to 7.615773106 and -7.615773106.


Subproblem 1
x + 7 = 7.615773106

Simplifying
x + 7 = 7.615773106

Reorder the terms:
7 + x = 7.615773106

Solving
7 + x = 7.615773106

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 = 7.615773106 + -7

Combine like terms: 7 + -7 = 0
0 + x = 7.615773106 + -7
x = 7.615773106 + -7

Combine like terms: 7.615773106 + -7 = 0.615773106
x = 0.615773106

Simplifying
x = 0.615773106


Subproblem 2
x + 7 = -7.615773106

Simplifying
x + 7 = -7.615773106

Reorder the terms:
7 + x = -7.615773106

Solving
7 + x = -7.615773106

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 = -7.615773106 + -7

Combine like terms: 7 + -7 = 0
0 + x = -7.615773106 + -7
x = -7.615773106 + -7

Combine like terms: -7.615773106 + -7 = -14.615773106
x = -14.615773106

Simplifying
x = -14.615773106


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.615773106, -14.615773106}

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