-16x^2-150x+250=0

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Solution for -16x^2-150x+250=0 equation: 


Simplifying
-16x2 + -150x + 250 = 0

Reorder the terms:
250 + -150x + -16x2 = 0

Solving
250 + -150x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(125 + -75x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(125 + -75x + -8x2)' equal to zero and attempt to solve:

Simplifying
125 + -75x + -8x2 = 0

Solving
125 + -75x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-15.625 + 9.375x + x2 = 0

Move the constant term to the right:

Add '15.625' to each side of the equation.
-15.625 + 9.375x + 15.625 + x2 = 0 + 15.625

Reorder the terms:
-15.625 + 15.625 + 9.375x + x2 = 0 + 15.625

Combine like terms: -15.625 + 15.625 = 0.000
0.000 + 9.375x + x2 = 0 + 15.625
9.375x + x2 = 0 + 15.625

Combine like terms: 0 + 15.625 = 15.625
9.375x + x2 = 15.625

The x term is 9.375x.  Take half its coefficient (4.6875).
Square it (21.97265625) and add it to both sides.

Add '21.97265625' to each side of the equation.
9.375x + 21.97265625 + x2 = 15.625 + 21.97265625

Reorder the terms:
21.97265625 + 9.375x + x2 = 15.625 + 21.97265625

Combine like terms: 15.625 + 21.97265625 = 37.59765625
21.97265625 + 9.375x + x2 = 37.59765625

Factor a perfect square on the left side:
(x + 4.6875)(x + 4.6875) = 37.59765625

Calculate the square root of the right side: 6.131692772

Break this problem into two subproblems by setting 
(x + 4.6875) equal to 6.131692772 and -6.131692772.


Subproblem 1
x + 4.6875 = 6.131692772

Simplifying
x + 4.6875 = 6.131692772

Reorder the terms:
4.6875 + x = 6.131692772

Solving
4.6875 + x = 6.131692772

Solving for variable 'x'.

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

Add '-4.6875' to each side of the equation.
4.6875 + -4.6875 + x = 6.131692772 + -4.6875

Combine like terms: 4.6875 + -4.6875 = 0.0000
0.0000 + x = 6.131692772 + -4.6875
x = 6.131692772 + -4.6875

Combine like terms: 6.131692772 + -4.6875 = 1.444192772
x = 1.444192772

Simplifying
x = 1.444192772


Subproblem 2
x + 4.6875 = -6.131692772

Simplifying
x + 4.6875 = -6.131692772

Reorder the terms:
4.6875 + x = -6.131692772

Solving
4.6875 + x = -6.131692772

Solving for variable 'x'.

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

Add '-4.6875' to each side of the equation.
4.6875 + -4.6875 + x = -6.131692772 + -4.6875

Combine like terms: 4.6875 + -4.6875 = 0.0000
0.0000 + x = -6.131692772 + -4.6875
x = -6.131692772 + -4.6875

Combine like terms: -6.131692772 + -4.6875 = -10.819192772
x = -10.819192772

Simplifying
x = -10.819192772


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.444192772, -10.819192772}
Solution
x = {1.444192772, -10.819192772}

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