-16x^2+24x+1500=0

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Solution for -16x^2+24x+1500=0 equation: 


Simplifying
-16x2 + 24x + 1500 = 0

Reorder the terms:
1500 + 24x + -16x2 = 0

Solving
1500 + 24x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(375 + 6x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(375 + 6x + -4x2)' equal to zero and attempt to solve:

Simplifying
375 + 6x + -4x2 = 0

Solving
375 + 6x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-93.75 + -1.5x + x2 = 0

Move the constant term to the right:

Add '93.75' to each side of the equation.
-93.75 + -1.5x + 93.75 + x2 = 0 + 93.75

Reorder the terms:
-93.75 + 93.75 + -1.5x + x2 = 0 + 93.75

Combine like terms: -93.75 + 93.75 = 0.00
0.00 + -1.5x + x2 = 0 + 93.75
-1.5x + x2 = 0 + 93.75

Combine like terms: 0 + 93.75 = 93.75
-1.5x + x2 = 93.75

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 93.75 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 93.75 + 0.5625

Combine like terms: 93.75 + 0.5625 = 94.3125
0.5625 + -1.5x + x2 = 94.3125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 94.3125

Calculate the square root of the right side: 9.7114623

Break this problem into two subproblems by setting 
(x + -0.75) equal to 9.7114623 and -9.7114623.


Subproblem 1
x + -0.75 = 9.7114623

Simplifying
x + -0.75 = 9.7114623

Reorder the terms:
-0.75 + x = 9.7114623

Solving
-0.75 + x = 9.7114623

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 9.7114623 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 9.7114623 + 0.75
x = 9.7114623 + 0.75

Combine like terms: 9.7114623 + 0.75 = 10.4614623
x = 10.4614623

Simplifying
x = 10.4614623


Subproblem 2
x + -0.75 = -9.7114623

Simplifying
x + -0.75 = -9.7114623

Reorder the terms:
-0.75 + x = -9.7114623

Solving
-0.75 + x = -9.7114623

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -9.7114623 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -9.7114623 + 0.75
x = -9.7114623 + 0.75

Combine like terms: -9.7114623 + 0.75 = -8.9614623
x = -8.9614623

Simplifying
x = -8.9614623


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.4614623, -8.9614623}
Solution
x = {10.4614623, -8.9614623}

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