-16x^2+112x-102=0

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Solution for -16x^2+112x-102=0 equation: 


Simplifying
-16x2 + 112x + -102 = 0

Reorder the terms:
-102 + 112x + -16x2 = 0

Solving
-102 + 112x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-51 + 56x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-51 + 56x + -8x2)' equal to zero and attempt to solve:

Simplifying
-51 + 56x + -8x2 = 0

Solving
-51 + 56x + -8x2 = 0

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

Divide each side by '-8'.
6.375 + -7x + x2 = 0

Move the constant term to the right:

Add '-6.375' to each side of the equation.
6.375 + -7x + -6.375 + x2 = 0 + -6.375

Reorder the terms:
6.375 + -6.375 + -7x + x2 = 0 + -6.375

Combine like terms: 6.375 + -6.375 = 0.000
0.000 + -7x + x2 = 0 + -6.375
-7x + x2 = 0 + -6.375

Combine like terms: 0 + -6.375 = -6.375
-7x + x2 = -6.375

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -6.375 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -6.375 + 12.25

Combine like terms: -6.375 + 12.25 = 5.875
12.25 + -7x + x2 = 5.875

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 5.875

Calculate the square root of the right side: 2.423839929

Break this problem into two subproblems by setting 
(x + -3.5) equal to 2.423839929 and -2.423839929.


Subproblem 1
x + -3.5 = 2.423839929

Simplifying
x + -3.5 = 2.423839929

Reorder the terms:
-3.5 + x = 2.423839929

Solving
-3.5 + x = 2.423839929

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 2.423839929 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 2.423839929 + 3.5
x = 2.423839929 + 3.5

Combine like terms: 2.423839929 + 3.5 = 5.923839929
x = 5.923839929

Simplifying
x = 5.923839929


Subproblem 2
x + -3.5 = -2.423839929

Simplifying
x + -3.5 = -2.423839929

Reorder the terms:
-3.5 + x = -2.423839929

Solving
-3.5 + x = -2.423839929

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -2.423839929 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -2.423839929 + 3.5
x = -2.423839929 + 3.5

Combine like terms: -2.423839929 + 3.5 = 1.076160071
x = 1.076160071

Simplifying
x = 1.076160071


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.923839929, 1.076160071}
Solution
x = {5.923839929, 1.076160071}

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