14x+x^2=180

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Solution for 14x+x^2=180 equation:


Simplifying
14x + x2 = 180

Solving
14x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 14x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 14x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + 14x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 14x + x2 = 0 + 180
14x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
14x + x2 = 180

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 = 180 + 49

Reorder the terms:
49 + 14x + x2 = 180 + 49

Combine like terms: 180 + 49 = 229
49 + 14x + x2 = 229

Factor a perfect square on the left side:
(x + 7)(x + 7) = 229

Calculate the square root of the right side: 15.13274595

Break this problem into two subproblems by setting 
(x + 7) equal to 15.13274595 and -15.13274595.

Subproblem 1

x + 7 = 15.13274595 Simplifying x + 7 = 15.13274595 Reorder the terms: 7 + x = 15.13274595 Solving 7 + x = 15.13274595 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 = 15.13274595 + -7 Combine like terms: 7 + -7 = 0 0 + x = 15.13274595 + -7 x = 15.13274595 + -7 Combine like terms: 15.13274595 + -7 = 8.13274595 x = 8.13274595 Simplifying x = 8.13274595

Subproblem 2

x + 7 = -15.13274595 Simplifying x + 7 = -15.13274595 Reorder the terms: 7 + x = -15.13274595 Solving 7 + x = -15.13274595 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 = -15.13274595 + -7 Combine like terms: 7 + -7 = 0 0 + x = -15.13274595 + -7 x = -15.13274595 + -7 Combine like terms: -15.13274595 + -7 = -22.13274595 x = -22.13274595 Simplifying x = -22.13274595

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.13274595, -22.13274595}

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