-16x^2+160x+18=0

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Solution for -16x^2+160x+18=0 equation: 


Simplifying
-16x2 + 160x + 18 = 0

Reorder the terms:
18 + 160x + -16x2 = 0

Solving
18 + 160x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 80x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + 80x + -8x2)' equal to zero and attempt to solve:

Simplifying
9 + 80x + -8x2 = 0

Solving
9 + 80x + -8x2 = 0

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

Divide each side by '-8'.
-1.125 + -10x + x2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -10x + 1.125 + x2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -10x + x2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -10x + x2 = 0 + 1.125
-10x + x2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-10x + x2 = 1.125

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 1.125 + 25

Reorder the terms:
25 + -10x + x2 = 1.125 + 25

Combine like terms: 1.125 + 25 = 26.125
25 + -10x + x2 = 26.125

Factor a perfect square on the left side:
(x + -5)(x + -5) = 26.125

Calculate the square root of the right side: 5.111262075

Break this problem into two subproblems by setting 
(x + -5) equal to 5.111262075 and -5.111262075.


Subproblem 1
x + -5 = 5.111262075

Simplifying
x + -5 = 5.111262075

Reorder the terms:
-5 + x = 5.111262075

Solving
-5 + x = 5.111262075

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 5.111262075 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.111262075 + 5
x = 5.111262075 + 5

Combine like terms: 5.111262075 + 5 = 10.111262075
x = 10.111262075

Simplifying
x = 10.111262075


Subproblem 2
x + -5 = -5.111262075

Simplifying
x + -5 = -5.111262075

Reorder the terms:
-5 + x = -5.111262075

Solving
-5 + x = -5.111262075

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -5.111262075 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.111262075 + 5
x = -5.111262075 + 5

Combine like terms: -5.111262075 + 5 = -0.111262075
x = -0.111262075

Simplifying
x = -0.111262075


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.111262075, -0.111262075}
Solution
x = {10.111262075, -0.111262075}

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