2x^2+92x-960=0

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Solution for 2x^2+92x-960=0 equation: 


Simplifying
2x2 + 92x + -960 = 0

Reorder the terms:
-960 + 92x + 2x2 = 0

Solving
-960 + 92x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-480 + 46x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-480 + 46x + x2)' equal to zero and attempt to solve:

Simplifying
-480 + 46x + x2 = 0

Solving
-480 + 46x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '480' to each side of the equation.
-480 + 46x + 480 + x2 = 0 + 480

Reorder the terms:
-480 + 480 + 46x + x2 = 0 + 480

Combine like terms: -480 + 480 = 0
0 + 46x + x2 = 0 + 480
46x + x2 = 0 + 480

Combine like terms: 0 + 480 = 480
46x + x2 = 480

The x term is 46x.  Take half its coefficient (23).
Square it (529) and add it to both sides.

Add '529' to each side of the equation.
46x + 529 + x2 = 480 + 529

Reorder the terms:
529 + 46x + x2 = 480 + 529

Combine like terms: 480 + 529 = 1009
529 + 46x + x2 = 1009

Factor a perfect square on the left side:
(x + 23)(x + 23) = 1009

Calculate the square root of the right side: 31.764760349

Break this problem into two subproblems by setting 
(x + 23) equal to 31.764760349 and -31.764760349.


Subproblem 1
x + 23 = 31.764760349

Simplifying
x + 23 = 31.764760349

Reorder the terms:
23 + x = 31.764760349

Solving
23 + x = 31.764760349

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-23' to each side of the equation.
23 + -23 + x = 31.764760349 + -23

Combine like terms: 23 + -23 = 0
0 + x = 31.764760349 + -23
x = 31.764760349 + -23

Combine like terms: 31.764760349 + -23 = 8.764760349
x = 8.764760349

Simplifying
x = 8.764760349


Subproblem 2
x + 23 = -31.764760349

Simplifying
x + 23 = -31.764760349

Reorder the terms:
23 + x = -31.764760349

Solving
23 + x = -31.764760349

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-23' to each side of the equation.
23 + -23 + x = -31.764760349 + -23

Combine like terms: 23 + -23 = 0
0 + x = -31.764760349 + -23
x = -31.764760349 + -23

Combine like terms: -31.764760349 + -23 = -54.764760349
x = -54.764760349

Simplifying
x = -54.764760349


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.764760349, -54.764760349}
Solution
x = {8.764760349, -54.764760349}

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