-16x^2+36x+160=0

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Solution for -16x^2+36x+160=0 equation: 


Simplifying
-16x2 + 36x + 160 = 0

Reorder the terms:
160 + 36x + -16x2 = 0

Solving
160 + 36x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(40 + 9x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(40 + 9x + -4x2)' equal to zero and attempt to solve:

Simplifying
40 + 9x + -4x2 = 0

Solving
40 + 9x + -4x2 = 0

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

Divide each side by '-4'.
-10 + -2.25x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2.25x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -2.25x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2.25x + x2 = 0 + 10
-2.25x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2.25x + x2 = 10

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 10 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 10 + 1.265625

Combine like terms: 10 + 1.265625 = 11.265625
1.265625 + -2.25x + x2 = 11.265625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 11.265625

Calculate the square root of the right side: 3.356430396

Break this problem into two subproblems by setting 
(x + -1.125) equal to 3.356430396 and -3.356430396.


Subproblem 1
x + -1.125 = 3.356430396

Simplifying
x + -1.125 = 3.356430396

Reorder the terms:
-1.125 + x = 3.356430396

Solving
-1.125 + x = 3.356430396

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 3.356430396 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 3.356430396 + 1.125
x = 3.356430396 + 1.125

Combine like terms: 3.356430396 + 1.125 = 4.481430396
x = 4.481430396

Simplifying
x = 4.481430396


Subproblem 2
x + -1.125 = -3.356430396

Simplifying
x + -1.125 = -3.356430396

Reorder the terms:
-1.125 + x = -3.356430396

Solving
-1.125 + x = -3.356430396

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -3.356430396 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -3.356430396 + 1.125
x = -3.356430396 + 1.125

Combine like terms: -3.356430396 + 1.125 = -2.231430396
x = -2.231430396

Simplifying
x = -2.231430396


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.481430396, -2.231430396}
Solution
x = {4.481430396, -2.231430396}

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