-.5x^2-25x-275=0

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Solution for -.5x^2-25x-275=0 equation:


Simplifying
-0.5x2 + -25x + -275 = 0

Reorder the terms:
-275 + -25x + -0.5x2 = 0

Solving
-275 + -25x + -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'.
550 + 50x + x2 = 0

Move the constant term to the right:

Add '-550' to each side of the equation.
550 + 50x + -550 + x2 = 0 + -550

Reorder the terms:
550 + -550 + 50x + x2 = 0 + -550

Combine like terms: 550 + -550 = 0
0 + 50x + x2 = 0 + -550
50x + x2 = 0 + -550

Combine like terms: 0 + -550 = -550
50x + x2 = -550

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = -550 + 625

Reorder the terms:
625 + 50x + x2 = -550 + 625

Combine like terms: -550 + 625 = 75
625 + 50x + x2 = 75

Factor a perfect square on the left side:
(x + 25)(x + 25) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + 25) equal to 8.660254038 and -8.660254038.


Subproblem 1
x + 25 = 8.660254038

Simplifying
x + 25 = 8.660254038

Reorder the terms:
25 + x = 8.660254038

Solving
25 + x = 8.660254038

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = 8.660254038 + -25

Combine like terms: 25 + -25 = 0
0 + x = 8.660254038 + -25
x = 8.660254038 + -25

Combine like terms: 8.660254038 + -25 = -16.339745962
x = -16.339745962

Simplifying
x = -16.339745962


Subproblem 2
x + 25 = -8.660254038

Simplifying
x + 25 = -8.660254038

Reorder the terms:
25 + x = -8.660254038

Solving
25 + x = -8.660254038

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = -8.660254038 + -25

Combine like terms: 25 + -25 = 0
0 + x = -8.660254038 + -25
x = -8.660254038 + -25

Combine like terms: -8.660254038 + -25 = -33.660254038
x = -33.660254038

Simplifying
x = -33.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-16.339745962, -33.660254038}

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