-16x^2-10x+400=0

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Solution for -16x^2-10x+400=0 equation: 


Simplifying
-16x2 + -10x + 400 = 0

Reorder the terms:
400 + -10x + -16x2 = 0

Solving
400 + -10x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(200 + -5x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(200 + -5x + -8x2)' equal to zero and attempt to solve:

Simplifying
200 + -5x + -8x2 = 0

Solving
200 + -5x + -8x2 = 0

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

Divide each side by '-8'.
-25 + 0.625x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 0.625x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 0.625x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 0.625x + x2 = 0 + 25
0.625x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
0.625x + x2 = 25

The x term is 0.625x.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625x + 0.09765625 + x2 = 25 + 0.09765625

Reorder the terms:
0.09765625 + 0.625x + x2 = 25 + 0.09765625

Combine like terms: 25 + 0.09765625 = 25.09765625
0.09765625 + 0.625x + x2 = 25.09765625

Factor a perfect square on the left side:
(x + 0.3125)(x + 0.3125) = 25.09765625

Calculate the square root of the right side: 5.009756107

Break this problem into two subproblems by setting 
(x + 0.3125) equal to 5.009756107 and -5.009756107.


Subproblem 1
x + 0.3125 = 5.009756107

Simplifying
x + 0.3125 = 5.009756107

Reorder the terms:
0.3125 + x = 5.009756107

Solving
0.3125 + x = 5.009756107

Solving for variable 'x'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + x = 5.009756107 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + x = 5.009756107 + -0.3125
x = 5.009756107 + -0.3125

Combine like terms: 5.009756107 + -0.3125 = 4.697256107
x = 4.697256107

Simplifying
x = 4.697256107


Subproblem 2
x + 0.3125 = -5.009756107

Simplifying
x + 0.3125 = -5.009756107

Reorder the terms:
0.3125 + x = -5.009756107

Solving
0.3125 + x = -5.009756107

Solving for variable 'x'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + x = -5.009756107 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + x = -5.009756107 + -0.3125
x = -5.009756107 + -0.3125

Combine like terms: -5.009756107 + -0.3125 = -5.322256107
x = -5.322256107

Simplifying
x = -5.322256107


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.697256107, -5.322256107}
Solution
x = {4.697256107, -5.322256107}

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