-16x^2+20x+15=0

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Solution for -16x^2+20x+15=0 equation:


Simplifying
-16x2 + 20x + 15 = 0

Reorder the terms:
15 + 20x + -16x2 = 0

Solving
15 + 20x + -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 + -1.25x + x2 = 0

Move the constant term to the right:

Add '0.9375' to each side of the equation.
-0.9375 + -1.25x + 0.9375 + x2 = 0 + 0.9375

Reorder the terms:
-0.9375 + 0.9375 + -1.25x + x2 = 0 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + -1.25x + x2 = 0 + 0.9375
-1.25x + x2 = 0 + 0.9375

Combine like terms: 0 + 0.9375 = 0.9375
-1.25x + x2 = 0.9375

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 0.9375 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 0.9375 + 0.390625

Combine like terms: 0.9375 + 0.390625 = 1.328125
0.390625 + -1.25x + x2 = 1.328125

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 1.328125

Calculate the square root of the right side: 1.152443057

Break this problem into two subproblems by setting 
(x + -0.625) equal to 1.152443057 and -1.152443057.

Subproblem 1

x + -0.625 = 1.152443057 Simplifying x + -0.625 = 1.152443057 Reorder the terms: -0.625 + x = 1.152443057 Solving -0.625 + x = 1.152443057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.152443057 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.152443057 + 0.625 x = 1.152443057 + 0.625 Combine like terms: 1.152443057 + 0.625 = 1.777443057 x = 1.777443057 Simplifying x = 1.777443057

Subproblem 2

x + -0.625 = -1.152443057 Simplifying x + -0.625 = -1.152443057 Reorder the terms: -0.625 + x = -1.152443057 Solving -0.625 + x = -1.152443057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.152443057 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.152443057 + 0.625 x = -1.152443057 + 0.625 Combine like terms: -1.152443057 + 0.625 = -0.527443057 x = -0.527443057 Simplifying x = -0.527443057

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.777443057, -0.527443057}

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