16x^2+22x-112=0

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Solution for 16x^2+22x-112=0 equation: 


Simplifying
16x2 + 22x + -112 = 0

Reorder the terms:
-112 + 22x + 16x2 = 0

Solving
-112 + 22x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-56 + 11x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-56 + 11x + 8x2)' equal to zero and attempt to solve:

Simplifying
-56 + 11x + 8x2 = 0

Solving
-56 + 11x + 8x2 = 0

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

Divide each side by '8'.
-7 + 1.375x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 1.375x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 1.375x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 1.375x + x2 = 0 + 7
1.375x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
1.375x + x2 = 7

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 = 7 + 0.47265625

Reorder the terms:
0.47265625 + 1.375x + x2 = 7 + 0.47265625

Combine like terms: 7 + 0.47265625 = 7.47265625
0.47265625 + 1.375x + x2 = 7.47265625

Factor a perfect square on the left side:
(x + 0.6875)(x + 0.6875) = 7.47265625

Calculate the square root of the right side: 2.733615966

Break this problem into two subproblems by setting 
(x + 0.6875) equal to 2.733615966 and -2.733615966.


Subproblem 1
x + 0.6875 = 2.733615966

Simplifying
x + 0.6875 = 2.733615966

Reorder the terms:
0.6875 + x = 2.733615966

Solving
0.6875 + x = 2.733615966

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 = 2.733615966 + -0.6875

Combine like terms: 0.6875 + -0.6875 = 0.0000
0.0000 + x = 2.733615966 + -0.6875
x = 2.733615966 + -0.6875

Combine like terms: 2.733615966 + -0.6875 = 2.046115966
x = 2.046115966

Simplifying
x = 2.046115966


Subproblem 2
x + 0.6875 = -2.733615966

Simplifying
x + 0.6875 = -2.733615966

Reorder the terms:
0.6875 + x = -2.733615966

Solving
0.6875 + x = -2.733615966

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 = -2.733615966 + -0.6875

Combine like terms: 0.6875 + -0.6875 = 0.0000
0.0000 + x = -2.733615966 + -0.6875
x = -2.733615966 + -0.6875

Combine like terms: -2.733615966 + -0.6875 = -3.421115966
x = -3.421115966

Simplifying
x = -3.421115966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.046115966, -3.421115966}
Solution
x = {2.046115966, -3.421115966}

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