16x^2-32x-15=0

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Solution for 16x^2-32x-15=0 equation:


Simplifying
16x2 + -32x + -15 = 0

Reorder the terms:
-15 + -32x + 16x2 = 0

Solving
-15 + -32x + 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 + -2x + x2 = 0

Move the constant term to the right:

Add '0.9375' to each side of the equation.
-0.9375 + -2x + 0.9375 + x2 = 0 + 0.9375

Reorder the terms:
-0.9375 + 0.9375 + -2x + x2 = 0 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + -2x + x2 = 0 + 0.9375
-2x + x2 = 0 + 0.9375

Combine like terms: 0 + 0.9375 = 0.9375
-2x + x2 = 0.9375

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 0.9375 + 1

Reorder the terms:
1 + -2x + x2 = 0.9375 + 1

Combine like terms: 0.9375 + 1 = 1.9375
1 + -2x + x2 = 1.9375

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.9375

Calculate the square root of the right side: 1.391941091

Break this problem into two subproblems by setting 
(x + -1) equal to 1.391941091 and -1.391941091.

Subproblem 1

x + -1 = 1.391941091 Simplifying x + -1 = 1.391941091 Reorder the terms: -1 + x = 1.391941091 Solving -1 + x = 1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.391941091 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.391941091 + 1 x = 1.391941091 + 1 Combine like terms: 1.391941091 + 1 = 2.391941091 x = 2.391941091 Simplifying x = 2.391941091

Subproblem 2

x + -1 = -1.391941091 Simplifying x + -1 = -1.391941091 Reorder the terms: -1 + x = -1.391941091 Solving -1 + x = -1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.391941091 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.391941091 + 1 x = -1.391941091 + 1 Combine like terms: -1.391941091 + 1 = -0.391941091 x = -0.391941091 Simplifying x = -0.391941091

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.391941091, -0.391941091}

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