-16x^2+40x+50=0

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Solution for -16x^2+40x+50=0 equation: 


Simplifying
-16x2 + 40x + 50 = 0

Reorder the terms:
50 + 40x + -16x2 = 0

Solving
50 + 40x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 20x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 20x + -8x2)' equal to zero and attempt to solve:

Simplifying
25 + 20x + -8x2 = 0

Solving
25 + 20x + -8x2 = 0

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

Divide each side by '-8'.
-3.125 + -2.5x + x2 = 0

Move the constant term to the right:

Add '3.125' to each side of the equation.
-3.125 + -2.5x + 3.125 + x2 = 0 + 3.125

Reorder the terms:
-3.125 + 3.125 + -2.5x + x2 = 0 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + -2.5x + x2 = 0 + 3.125
-2.5x + x2 = 0 + 3.125

Combine like terms: 0 + 3.125 = 3.125
-2.5x + x2 = 3.125

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 3.125 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 3.125 + 1.5625

Combine like terms: 3.125 + 1.5625 = 4.6875
1.5625 + -2.5x + x2 = 4.6875

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 4.6875

Calculate the square root of the right side: 2.165063509

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.165063509 and -2.165063509.


Subproblem 1
x + -1.25 = 2.165063509

Simplifying
x + -1.25 = 2.165063509

Reorder the terms:
-1.25 + x = 2.165063509

Solving
-1.25 + x = 2.165063509

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 2.165063509 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 2.165063509 + 1.25
x = 2.165063509 + 1.25

Combine like terms: 2.165063509 + 1.25 = 3.415063509
x = 3.415063509

Simplifying
x = 3.415063509


Subproblem 2
x + -1.25 = -2.165063509

Simplifying
x + -1.25 = -2.165063509

Reorder the terms:
-1.25 + x = -2.165063509

Solving
-1.25 + x = -2.165063509

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -2.165063509 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -2.165063509 + 1.25
x = -2.165063509 + 1.25

Combine like terms: -2.165063509 + 1.25 = -0.915063509
x = -0.915063509

Simplifying
x = -0.915063509


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.415063509, -0.915063509}
Solution
x = {3.415063509, -0.915063509}

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