-16x^2+9x+15=0

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Solution for -16x^2+9x+15=0 equation:


Simplifying
-16x2 + 9x + 15 = 0

Reorder the terms:
15 + 9x + -16x2 = 0

Solving
15 + 9x + -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'.
-0.9375 + -0.5625x + x2 = 0

Move the constant term to the right:

Add '0.9375' to each side of the equation.
-0.9375 + -0.5625x + 0.9375 + x2 = 0 + 0.9375

Reorder the terms:
-0.9375 + 0.9375 + -0.5625x + x2 = 0 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + -0.5625x + x2 = 0 + 0.9375
-0.5625x + x2 = 0 + 0.9375

Combine like terms: 0 + 0.9375 = 0.9375
-0.5625x + x2 = 0.9375

The x term is -0.5625x.  Take half its coefficient (-0.28125).
Square it (0.0791015625) and add it to both sides.

Add '0.0791015625' to each side of the equation.
-0.5625x + 0.0791015625 + x2 = 0.9375 + 0.0791015625

Reorder the terms:
0.0791015625 + -0.5625x + x2 = 0.9375 + 0.0791015625

Combine like terms: 0.9375 + 0.0791015625 = 1.0166015625
0.0791015625 + -0.5625x + x2 = 1.0166015625

Factor a perfect square on the left side:
(x + -0.28125)(x + -0.28125) = 1.0166015625

Calculate the square root of the right side: 1.008266613

Break this problem into two subproblems by setting 
(x + -0.28125) equal to 1.008266613 and -1.008266613.

Subproblem 1

x + -0.28125 = 1.008266613 Simplifying x + -0.28125 = 1.008266613 Reorder the terms: -0.28125 + x = 1.008266613 Solving -0.28125 + x = 1.008266613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = 1.008266613 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = 1.008266613 + 0.28125 x = 1.008266613 + 0.28125 Combine like terms: 1.008266613 + 0.28125 = 1.289516613 x = 1.289516613 Simplifying x = 1.289516613

Subproblem 2

x + -0.28125 = -1.008266613 Simplifying x + -0.28125 = -1.008266613 Reorder the terms: -0.28125 + x = -1.008266613 Solving -0.28125 + x = -1.008266613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = -1.008266613 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = -1.008266613 + 0.28125 x = -1.008266613 + 0.28125 Combine like terms: -1.008266613 + 0.28125 = -0.727016613 x = -0.727016613 Simplifying x = -0.727016613

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.289516613, -0.727016613}

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