-16x^2+96x+13=0

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Solution for -16x^2+96x+13=0 equation:


Simplifying
-16x2 + 96x + 13 = 0

Reorder the terms:
13 + 96x + -16x2 = 0

Solving
13 + 96x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.8125 + -6x + x2 = 0

Move the constant term to the right:

Add '0.8125' to each side of the equation.
-0.8125 + -6x + 0.8125 + x2 = 0 + 0.8125

Reorder the terms:
-0.8125 + 0.8125 + -6x + x2 = 0 + 0.8125

Combine like terms: -0.8125 + 0.8125 = 0.0000
0.0000 + -6x + x2 = 0 + 0.8125
-6x + x2 = 0 + 0.8125

Combine like terms: 0 + 0.8125 = 0.8125
-6x + x2 = 0.8125

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 0.8125 + 9

Reorder the terms:
9 + -6x + x2 = 0.8125 + 9

Combine like terms: 0.8125 + 9 = 9.8125
9 + -6x + x2 = 9.8125

Factor a perfect square on the left side:
(x + -3)(x + -3) = 9.8125

Calculate the square root of the right side: 3.132491022

Break this problem into two subproblems by setting 
(x + -3) equal to 3.132491022 and -3.132491022.

Subproblem 1

x + -3 = 3.132491022 Simplifying x + -3 = 3.132491022 Reorder the terms: -3 + x = 3.132491022 Solving -3 + x = 3.132491022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.132491022 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.132491022 + 3 x = 3.132491022 + 3 Combine like terms: 3.132491022 + 3 = 6.132491022 x = 6.132491022 Simplifying x = 6.132491022

Subproblem 2

x + -3 = -3.132491022 Simplifying x + -3 = -3.132491022 Reorder the terms: -3 + x = -3.132491022 Solving -3 + x = -3.132491022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.132491022 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.132491022 + 3 x = -3.132491022 + 3 Combine like terms: -3.132491022 + 3 = -0.132491022 x = -0.132491022 Simplifying x = -0.132491022

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.132491022, -0.132491022}

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