-16x^2+12x+310=0

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Solution for -16x^2+12x+310=0 equation: 


Simplifying
-16x2 + 12x + 310 = 0

Reorder the terms:
310 + 12x + -16x2 = 0

Solving
310 + 12x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(155 + 6x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(155 + 6x + -8x2)' equal to zero and attempt to solve:

Simplifying
155 + 6x + -8x2 = 0

Solving
155 + 6x + -8x2 = 0

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

Divide each side by '-8'.
-19.375 + -0.75x + x2 = 0

Move the constant term to the right:

Add '19.375' to each side of the equation.
-19.375 + -0.75x + 19.375 + x2 = 0 + 19.375

Reorder the terms:
-19.375 + 19.375 + -0.75x + x2 = 0 + 19.375

Combine like terms: -19.375 + 19.375 = 0.000
0.000 + -0.75x + x2 = 0 + 19.375
-0.75x + x2 = 0 + 19.375

Combine like terms: 0 + 19.375 = 19.375
-0.75x + x2 = 19.375

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 19.375 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 19.375 + 0.140625

Combine like terms: 19.375 + 0.140625 = 19.515625
0.140625 + -0.75x + x2 = 19.515625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 19.515625

Calculate the square root of the right side: 4.417649262

Break this problem into two subproblems by setting 
(x + -0.375) equal to 4.417649262 and -4.417649262.


Subproblem 1
x + -0.375 = 4.417649262

Simplifying
x + -0.375 = 4.417649262

Reorder the terms:
-0.375 + x = 4.417649262

Solving
-0.375 + x = 4.417649262

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 4.417649262 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 4.417649262 + 0.375
x = 4.417649262 + 0.375

Combine like terms: 4.417649262 + 0.375 = 4.792649262
x = 4.792649262

Simplifying
x = 4.792649262


Subproblem 2
x + -0.375 = -4.417649262

Simplifying
x + -0.375 = -4.417649262

Reorder the terms:
-0.375 + x = -4.417649262

Solving
-0.375 + x = -4.417649262

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -4.417649262 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -4.417649262 + 0.375
x = -4.417649262 + 0.375

Combine like terms: -4.417649262 + 0.375 = -4.042649262
x = -4.042649262

Simplifying
x = -4.042649262


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.792649262, -4.042649262}
Solution
x = {4.792649262, -4.042649262}

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