16x^2+20x-200=0

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Solution for 16x^2+20x-200=0 equation: 


Simplifying
16x2 + 20x + -200 = 0

Reorder the terms:
-200 + 20x + 16x2 = 0

Solving
-200 + 20x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-50 + 5x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-50 + 5x + 4x2)' equal to zero and attempt to solve:

Simplifying
-50 + 5x + 4x2 = 0

Solving
-50 + 5x + 4x2 = 0

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

Divide each side by '4'.
-12.5 + 1.25x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 1.25x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 1.25x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 1.25x + x2 = 0 + 12.5
1.25x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
1.25x + x2 = 12.5

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 12.5 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 12.5 + 0.390625

Combine like terms: 12.5 + 0.390625 = 12.890625
0.390625 + 1.25x + x2 = 12.890625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 12.890625

Calculate the square root of the right side: 3.590351654

Break this problem into two subproblems by setting 
(x + 0.625) equal to 3.590351654 and -3.590351654.


Subproblem 1
x + 0.625 = 3.590351654

Simplifying
x + 0.625 = 3.590351654

Reorder the terms:
0.625 + x = 3.590351654

Solving
0.625 + x = 3.590351654

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 3.590351654 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 3.590351654 + -0.625
x = 3.590351654 + -0.625

Combine like terms: 3.590351654 + -0.625 = 2.965351654
x = 2.965351654

Simplifying
x = 2.965351654


Subproblem 2
x + 0.625 = -3.590351654

Simplifying
x + 0.625 = -3.590351654

Reorder the terms:
0.625 + x = -3.590351654

Solving
0.625 + x = -3.590351654

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -3.590351654 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -3.590351654 + -0.625
x = -3.590351654 + -0.625

Combine like terms: -3.590351654 + -0.625 = -4.215351654
x = -4.215351654

Simplifying
x = -4.215351654


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.965351654, -4.215351654}
Solution
x = {2.965351654, -4.215351654}

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