x^2+14x-225=0

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Solution for x^2+14x-225=0 equation: 


Simplifying
x2 + 14x + -225 = 0

Reorder the terms:
-225 + 14x + x2 = 0

Solving
-225 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + 14x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + 14x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + 14x + x2 = 0 + 225
14x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
14x + x2 = 225

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 = 225 + 49

Reorder the terms:
49 + 14x + x2 = 225 + 49

Combine like terms: 225 + 49 = 274
49 + 14x + x2 = 274

Factor a perfect square on the left side:
(x + 7)(x + 7) = 274

Calculate the square root of the right side: 16.552945357

Break this problem into two subproblems by setting 
(x + 7) equal to 16.552945357 and -16.552945357.


Subproblem 1
x + 7 = 16.552945357

Simplifying
x + 7 = 16.552945357

Reorder the terms:
7 + x = 16.552945357

Solving
7 + x = 16.552945357

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 = 16.552945357 + -7

Combine like terms: 7 + -7 = 0
0 + x = 16.552945357 + -7
x = 16.552945357 + -7

Combine like terms: 16.552945357 + -7 = 9.552945357
x = 9.552945357

Simplifying
x = 9.552945357


Subproblem 2
x + 7 = -16.552945357

Simplifying
x + 7 = -16.552945357

Reorder the terms:
7 + x = -16.552945357

Solving
7 + x = -16.552945357

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 = -16.552945357 + -7

Combine like terms: 7 + -7 = 0
0 + x = -16.552945357 + -7
x = -16.552945357 + -7

Combine like terms: -16.552945357 + -7 = -23.552945357
x = -23.552945357

Simplifying
x = -23.552945357


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.552945357, -23.552945357}

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