-16x^2+22x+220=0

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Solution for -16x^2+22x+220=0 equation: 


Simplifying
-16x2 + 22x + 220 = 0

Reorder the terms:
220 + 22x + -16x2 = 0

Solving
220 + 22x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(110 + 11x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(110 + 11x + -8x2)' equal to zero and attempt to solve:

Simplifying
110 + 11x + -8x2 = 0

Solving
110 + 11x + -8x2 = 0

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

Divide each side by '-8'.
-13.75 + -1.375x + x2 = 0

Move the constant term to the right:

Add '13.75' to each side of the equation.
-13.75 + -1.375x + 13.75 + x2 = 0 + 13.75

Reorder the terms:
-13.75 + 13.75 + -1.375x + x2 = 0 + 13.75

Combine like terms: -13.75 + 13.75 = 0.00
0.00 + -1.375x + x2 = 0 + 13.75
-1.375x + x2 = 0 + 13.75

Combine like terms: 0 + 13.75 = 13.75
-1.375x + x2 = 13.75

The x term is -1.375x.  Take half its coefficient (-0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
-1.375x + 0.47265625 + x2 = 13.75 + 0.47265625

Reorder the terms:
0.47265625 + -1.375x + x2 = 13.75 + 0.47265625

Combine like terms: 13.75 + 0.47265625 = 14.22265625
0.47265625 + -1.375x + x2 = 14.22265625

Factor a perfect square on the left side:
(x + -0.6875)(x + -0.6875) = 14.22265625

Calculate the square root of the right side: 3.77129371

Break this problem into two subproblems by setting 
(x + -0.6875) equal to 3.77129371 and -3.77129371.


Subproblem 1
x + -0.6875 = 3.77129371

Simplifying
x + -0.6875 = 3.77129371

Reorder the terms:
-0.6875 + x = 3.77129371

Solving
-0.6875 + x = 3.77129371

Solving for variable 'x'.

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

Add '0.6875' to each side of the equation.
-0.6875 + 0.6875 + x = 3.77129371 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + x = 3.77129371 + 0.6875
x = 3.77129371 + 0.6875

Combine like terms: 3.77129371 + 0.6875 = 4.45879371
x = 4.45879371

Simplifying
x = 4.45879371


Subproblem 2
x + -0.6875 = -3.77129371

Simplifying
x + -0.6875 = -3.77129371

Reorder the terms:
-0.6875 + x = -3.77129371

Solving
-0.6875 + x = -3.77129371

Solving for variable 'x'.

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

Add '0.6875' to each side of the equation.
-0.6875 + 0.6875 + x = -3.77129371 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + x = -3.77129371 + 0.6875
x = -3.77129371 + 0.6875

Combine like terms: -3.77129371 + 0.6875 = -3.08379371
x = -3.08379371

Simplifying
x = -3.08379371


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.45879371, -3.08379371}
Solution
x = {4.45879371, -3.08379371}

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