-8x^2+6x+3=0

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Solution for -8x^2+6x+3=0 equation:


Simplifying
-8x2 + 6x + 3 = 0

Reorder the terms:
3 + 6x + -8x2 = 0

Solving
3 + 6x + -8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.375 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -0.75x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -0.75x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -0.75x + x2 = 0 + 0.375
-0.75x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-0.75x + x2 = 0.375

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 0.375 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 0.375 + 0.140625

Combine like terms: 0.375 + 0.140625 = 0.515625
0.140625 + -0.75x + x2 = 0.515625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.718070331 and -0.718070331.

Subproblem 1

x + -0.375 = 0.718070331 Simplifying x + -0.375 = 0.718070331 Reorder the terms: -0.375 + x = 0.718070331 Solving -0.375 + x = 0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.718070331 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.718070331 + 0.375 x = 0.718070331 + 0.375 Combine like terms: 0.718070331 + 0.375 = 1.093070331 x = 1.093070331 Simplifying x = 1.093070331

Subproblem 2

x + -0.375 = -0.718070331 Simplifying x + -0.375 = -0.718070331 Reorder the terms: -0.375 + x = -0.718070331 Solving -0.375 + x = -0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.718070331 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.718070331 + 0.375 x = -0.718070331 + 0.375 Combine like terms: -0.718070331 + 0.375 = -0.343070331 x = -0.343070331 Simplifying x = -0.343070331

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.093070331, -0.343070331}

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