x^2+14x=960

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Solution for x^2+14x=960 equation: 


Simplifying
x2 + 14x = 960

Reorder the terms:
14x + x2 = 960

Solving
14x + x2 = 960

Solving for variable 'x'.

Reorder the terms:
-960 + 14x + x2 = 960 + -960

Combine like terms: 960 + -960 = 0
-960 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '960' to each side of the equation.
-960 + 14x + 960 + x2 = 0 + 960

Reorder the terms:
-960 + 960 + 14x + x2 = 0 + 960

Combine like terms: -960 + 960 = 0
0 + 14x + x2 = 0 + 960
14x + x2 = 0 + 960

Combine like terms: 0 + 960 = 960
14x + x2 = 960

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 = 960 + 49

Reorder the terms:
49 + 14x + x2 = 960 + 49

Combine like terms: 960 + 49 = 1009
49 + 14x + x2 = 1009

Factor a perfect square on the left side:
(x + 7)(x + 7) = 1009

Calculate the square root of the right side: 31.764760349

Break this problem into two subproblems by setting 
(x + 7) equal to 31.764760349 and -31.764760349.


Subproblem 1
x + 7 = 31.764760349

Simplifying
x + 7 = 31.764760349

Reorder the terms:
7 + x = 31.764760349

Solving
7 + x = 31.764760349

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 = 31.764760349 + -7

Combine like terms: 7 + -7 = 0
0 + x = 31.764760349 + -7
x = 31.764760349 + -7

Combine like terms: 31.764760349 + -7 = 24.764760349
x = 24.764760349

Simplifying
x = 24.764760349


Subproblem 2
x + 7 = -31.764760349

Simplifying
x + 7 = -31.764760349

Reorder the terms:
7 + x = -31.764760349

Solving
7 + x = -31.764760349

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 = -31.764760349 + -7

Combine like terms: 7 + -7 = 0
0 + x = -31.764760349 + -7
x = -31.764760349 + -7

Combine like terms: -31.764760349 + -7 = -38.764760349
x = -38.764760349

Simplifying
x = -38.764760349


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.764760349, -38.764760349}

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