-0.5x^2+176x-1440=0

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Solution for -0.5x^2+176x-1440=0 equation: 


Simplifying
-0.5x2 + 176x + -1440 = 0

Reorder the terms:
-1440 + 176x + -0.5x2 = 0

Solving
-1440 + 176x + -0.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
2880 + -352x + x2 = 0

Move the constant term to the right:

Add '-2880' to each side of the equation.
2880 + -352x + -2880 + x2 = 0 + -2880

Reorder the terms:
2880 + -2880 + -352x + x2 = 0 + -2880

Combine like terms: 2880 + -2880 = 0
0 + -352x + x2 = 0 + -2880
-352x + x2 = 0 + -2880

Combine like terms: 0 + -2880 = -2880
-352x + x2 = -2880

The x term is -352x.  Take half its coefficient (-176).
Square it (30976) and add it to both sides.

Add '30976' to each side of the equation.
-352x + 30976 + x2 = -2880 + 30976

Reorder the terms:
30976 + -352x + x2 = -2880 + 30976

Combine like terms: -2880 + 30976 = 28096
30976 + -352x + x2 = 28096

Factor a perfect square on the left side:
(x + -176)(x + -176) = 28096

Calculate the square root of the right side: 167.618614718

Break this problem into two subproblems by setting 
(x + -176) equal to 167.618614718 and -167.618614718.


Subproblem 1
x + -176 = 167.618614718

Simplifying
x + -176 = 167.618614718

Reorder the terms:
-176 + x = 167.618614718

Solving
-176 + x = 167.618614718

Solving for variable 'x'.

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

Add '176' to each side of the equation.
-176 + 176 + x = 167.618614718 + 176

Combine like terms: -176 + 176 = 0
0 + x = 167.618614718 + 176
x = 167.618614718 + 176

Combine like terms: 167.618614718 + 176 = 343.618614718
x = 343.618614718

Simplifying
x = 343.618614718


Subproblem 2
x + -176 = -167.618614718

Simplifying
x + -176 = -167.618614718

Reorder the terms:
-176 + x = -167.618614718

Solving
-176 + x = -167.618614718

Solving for variable 'x'.

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

Add '176' to each side of the equation.
-176 + 176 + x = -167.618614718 + 176

Combine like terms: -176 + 176 = 0
0 + x = -167.618614718 + 176
x = -167.618614718 + 176

Combine like terms: -167.618614718 + 176 = 8.381385282
x = 8.381385282

Simplifying
x = 8.381385282


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {343.618614718, 8.381385282}

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