-16x^2+200x-540=0

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Solution for -16x^2+200x-540=0 equation: 


Simplifying
-16x2 + 200x + -540 = 0

Reorder the terms:
-540 + 200x + -16x2 = 0

Solving
-540 + 200x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-135 + 50x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-135 + 50x + -4x2)' equal to zero and attempt to solve:

Simplifying
-135 + 50x + -4x2 = 0

Solving
-135 + 50x + -4x2 = 0

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

Divide each side by '-4'.
33.75 + -12.5x + x2 = 0

Move the constant term to the right:

Add '-33.75' to each side of the equation.
33.75 + -12.5x + -33.75 + x2 = 0 + -33.75

Reorder the terms:
33.75 + -33.75 + -12.5x + x2 = 0 + -33.75

Combine like terms: 33.75 + -33.75 = 0.00
0.00 + -12.5x + x2 = 0 + -33.75
-12.5x + x2 = 0 + -33.75

Combine like terms: 0 + -33.75 = -33.75
-12.5x + x2 = -33.75

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -33.75 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -33.75 + 39.0625

Combine like terms: -33.75 + 39.0625 = 5.3125
39.0625 + -12.5x + x2 = 5.3125

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 5.3125

Calculate the square root of the right side: 2.304886114

Break this problem into two subproblems by setting 
(x + -6.25) equal to 2.304886114 and -2.304886114.


Subproblem 1
x + -6.25 = 2.304886114

Simplifying
x + -6.25 = 2.304886114

Reorder the terms:
-6.25 + x = 2.304886114

Solving
-6.25 + x = 2.304886114

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 2.304886114 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 2.304886114 + 6.25
x = 2.304886114 + 6.25

Combine like terms: 2.304886114 + 6.25 = 8.554886114
x = 8.554886114

Simplifying
x = 8.554886114


Subproblem 2
x + -6.25 = -2.304886114

Simplifying
x + -6.25 = -2.304886114

Reorder the terms:
-6.25 + x = -2.304886114

Solving
-6.25 + x = -2.304886114

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -2.304886114 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -2.304886114 + 6.25
x = -2.304886114 + 6.25

Combine like terms: -2.304886114 + 6.25 = 3.945113886
x = 3.945113886

Simplifying
x = 3.945113886


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.554886114, 3.945113886}
Solution
x = {8.554886114, 3.945113886}

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