-16x^2+28x+230=0

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Solution for -16x^2+28x+230=0 equation: 


Simplifying
-16x2 + 28x + 230 = 0

Reorder the terms:
230 + 28x + -16x2 = 0

Solving
230 + 28x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(115 + 14x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(115 + 14x + -8x2)' equal to zero and attempt to solve:

Simplifying
115 + 14x + -8x2 = 0

Solving
115 + 14x + -8x2 = 0

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

Divide each side by '-8'.
-14.375 + -1.75x + x2 = 0

Move the constant term to the right:

Add '14.375' to each side of the equation.
-14.375 + -1.75x + 14.375 + x2 = 0 + 14.375

Reorder the terms:
-14.375 + 14.375 + -1.75x + x2 = 0 + 14.375

Combine like terms: -14.375 + 14.375 = 0.000
0.000 + -1.75x + x2 = 0 + 14.375
-1.75x + x2 = 0 + 14.375

Combine like terms: 0 + 14.375 = 14.375
-1.75x + x2 = 14.375

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 14.375 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 14.375 + 0.765625

Combine like terms: 14.375 + 0.765625 = 15.140625
0.765625 + -1.75x + x2 = 15.140625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 15.140625

Calculate the square root of the right side: 3.891095604

Break this problem into two subproblems by setting 
(x + -0.875) equal to 3.891095604 and -3.891095604.


Subproblem 1
x + -0.875 = 3.891095604

Simplifying
x + -0.875 = 3.891095604

Reorder the terms:
-0.875 + x = 3.891095604

Solving
-0.875 + x = 3.891095604

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 3.891095604 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 3.891095604 + 0.875
x = 3.891095604 + 0.875

Combine like terms: 3.891095604 + 0.875 = 4.766095604
x = 4.766095604

Simplifying
x = 4.766095604


Subproblem 2
x + -0.875 = -3.891095604

Simplifying
x + -0.875 = -3.891095604

Reorder the terms:
-0.875 + x = -3.891095604

Solving
-0.875 + x = -3.891095604

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -3.891095604 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -3.891095604 + 0.875
x = -3.891095604 + 0.875

Combine like terms: -3.891095604 + 0.875 = -3.016095604
x = -3.016095604

Simplifying
x = -3.016095604


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.766095604, -3.016095604}
Solution
x = {4.766095604, -3.016095604}

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