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

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


Simplifying
-16x2 + 250x + 150 = 0

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

Solving
150 + 250x + -16x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

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

Simplifying
75 + 125x + -8x2 = 0

Solving
75 + 125x + -8x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The x term is -15.625x.  Take half its coefficient (-7.8125).
Square it (61.03515625) and add it to both sides.

Add '61.03515625' to each side of the equation.
-15.625x + 61.03515625 + x2 = 9.375 + 61.03515625

Reorder the terms:
61.03515625 + -15.625x + x2 = 9.375 + 61.03515625

Combine like terms: 9.375 + 61.03515625 = 70.41015625
61.03515625 + -15.625x + x2 = 70.41015625

Factor a perfect square on the left side:
(x + -7.8125)(x + -7.8125) = 70.41015625

Calculate the square root of the right side: 8.391075989

Break this problem into two subproblems by setting 
(x + -7.8125) equal to 8.391075989 and -8.391075989.


Subproblem 1
x + -7.8125 = 8.391075989

Simplifying
x + -7.8125 = 8.391075989

Reorder the terms:
-7.8125 + x = 8.391075989

Solving
-7.8125 + x = 8.391075989

Solving for variable 'x'.

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

Add '7.8125' to each side of the equation.
-7.8125 + 7.8125 + x = 8.391075989 + 7.8125

Combine like terms: -7.8125 + 7.8125 = 0.0000
0.0000 + x = 8.391075989 + 7.8125
x = 8.391075989 + 7.8125

Combine like terms: 8.391075989 + 7.8125 = 16.203575989
x = 16.203575989

Simplifying
x = 16.203575989


Subproblem 2
x + -7.8125 = -8.391075989

Simplifying
x + -7.8125 = -8.391075989

Reorder the terms:
-7.8125 + x = -8.391075989

Solving
-7.8125 + x = -8.391075989

Solving for variable 'x'.

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

Add '7.8125' to each side of the equation.
-7.8125 + 7.8125 + x = -8.391075989 + 7.8125

Combine like terms: -7.8125 + 7.8125 = 0.0000
0.0000 + x = -8.391075989 + 7.8125
x = -8.391075989 + 7.8125

Combine like terms: -8.391075989 + 7.8125 = -0.578575989
x = -0.578575989

Simplifying
x = -0.578575989


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.203575989, -0.578575989}
Solution
x = {16.203575989, -0.578575989}

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