-16x^2+15x+6=0

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Solution for -16x^2+15x+6=0 equation:


Simplifying
-16x2 + 15x + 6 = 0

Reorder the terms:
6 + 15x + -16x2 = 0

Solving
6 + 15x + -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'.
-0.375 + -0.9375x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -0.9375x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -0.9375x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -0.9375x + x2 = 0 + 0.375
-0.9375x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-0.9375x + x2 = 0.375

The x term is -0.9375x.  Take half its coefficient (-0.46875).
Square it (0.2197265625) and add it to both sides.

Add '0.2197265625' to each side of the equation.
-0.9375x + 0.2197265625 + x2 = 0.375 + 0.2197265625

Reorder the terms:
0.2197265625 + -0.9375x + x2 = 0.375 + 0.2197265625

Combine like terms: 0.375 + 0.2197265625 = 0.5947265625
0.2197265625 + -0.9375x + x2 = 0.5947265625

Factor a perfect square on the left side:
(x + -0.46875)(x + -0.46875) = 0.5947265625

Calculate the square root of the right side: 0.771185167

Break this problem into two subproblems by setting 
(x + -0.46875) equal to 0.771185167 and -0.771185167.

Subproblem 1

x + -0.46875 = 0.771185167 Simplifying x + -0.46875 = 0.771185167 Reorder the terms: -0.46875 + x = 0.771185167 Solving -0.46875 + x = 0.771185167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + x = 0.771185167 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = 0.771185167 + 0.46875 x = 0.771185167 + 0.46875 Combine like terms: 0.771185167 + 0.46875 = 1.239935167 x = 1.239935167 Simplifying x = 1.239935167

Subproblem 2

x + -0.46875 = -0.771185167 Simplifying x + -0.46875 = -0.771185167 Reorder the terms: -0.46875 + x = -0.771185167 Solving -0.46875 + x = -0.771185167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + x = -0.771185167 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = -0.771185167 + 0.46875 x = -0.771185167 + 0.46875 Combine like terms: -0.771185167 + 0.46875 = -0.302435167 x = -0.302435167 Simplifying x = -0.302435167

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.239935167, -0.302435167}

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