-16x^2+16x+1000=0

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Solution for -16x^2+16x+1000=0 equation: 


Simplifying
-16x2 + 16x + 1000 = 0

Reorder the terms:
1000 + 16x + -16x2 = 0

Solving
1000 + 16x + -16x2 = 0

Solving for variable 'x'.

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

Ignore the factor 8.

Subproblem 1
Set the factor '(125 + 2x + -2x2)' equal to zero and attempt to solve:

Simplifying
125 + 2x + -2x2 = 0

Solving
125 + 2x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-62.5 + -1x + x2 = 0

Move the constant term to the right:

Add '62.5' to each side of the equation.
-62.5 + -1x + 62.5 + x2 = 0 + 62.5

Reorder the terms:
-62.5 + 62.5 + -1x + x2 = 0 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + -1x + x2 = 0 + 62.5
-1x + x2 = 0 + 62.5

Combine like terms: 0 + 62.5 = 62.5
-1x + x2 = 62.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 62.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 62.5 + 0.25

Combine like terms: 62.5 + 0.25 = 62.75
0.25 + -1x + x2 = 62.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 62.75

Calculate the square root of the right side: 7.921489759

Break this problem into two subproblems by setting 
(x + -0.5) equal to 7.921489759 and -7.921489759.


Subproblem 1
x + -0.5 = 7.921489759

Simplifying
x + -0.5 = 7.921489759

Reorder the terms:
-0.5 + x = 7.921489759

Solving
-0.5 + x = 7.921489759

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 7.921489759 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 7.921489759 + 0.5
x = 7.921489759 + 0.5

Combine like terms: 7.921489759 + 0.5 = 8.421489759
x = 8.421489759

Simplifying
x = 8.421489759


Subproblem 2
x + -0.5 = -7.921489759

Simplifying
x + -0.5 = -7.921489759

Reorder the terms:
-0.5 + x = -7.921489759

Solving
-0.5 + x = -7.921489759

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -7.921489759 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -7.921489759 + 0.5
x = -7.921489759 + 0.5

Combine like terms: -7.921489759 + 0.5 = -7.421489759
x = -7.421489759

Simplifying
x = -7.421489759


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.421489759, -7.421489759}
Solution
x = {8.421489759, -7.421489759}

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