-8x^2+5x+5=0

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Solution for -8x^2+5x+5=0 equation:


Simplifying
-8x2 + 5x + 5 = 0

Reorder the terms:
5 + 5x + -8x2 = 0

Solving
5 + 5x + -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'.
-0.625 + -0.625x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -0.625x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -0.625x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -0.625x + x2 = 0 + 0.625
-0.625x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-0.625x + x2 = 0.625

The x term is -0.625x.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625x + 0.09765625 + x2 = 0.625 + 0.09765625

Reorder the terms:
0.09765625 + -0.625x + x2 = 0.625 + 0.09765625

Combine like terms: 0.625 + 0.09765625 = 0.72265625
0.09765625 + -0.625x + x2 = 0.72265625

Factor a perfect square on the left side:
(x + -0.3125)(x + -0.3125) = 0.72265625

Calculate the square root of the right side: 0.850091907

Break this problem into two subproblems by setting 
(x + -0.3125) equal to 0.850091907 and -0.850091907.

Subproblem 1

x + -0.3125 = 0.850091907 Simplifying x + -0.3125 = 0.850091907 Reorder the terms: -0.3125 + x = 0.850091907 Solving -0.3125 + x = 0.850091907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 0.850091907 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 0.850091907 + 0.3125 x = 0.850091907 + 0.3125 Combine like terms: 0.850091907 + 0.3125 = 1.162591907 x = 1.162591907 Simplifying x = 1.162591907

Subproblem 2

x + -0.3125 = -0.850091907 Simplifying x + -0.3125 = -0.850091907 Reorder the terms: -0.3125 + x = -0.850091907 Solving -0.3125 + x = -0.850091907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -0.850091907 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -0.850091907 + 0.3125 x = -0.850091907 + 0.3125 Combine like terms: -0.850091907 + 0.3125 = -0.537591907 x = -0.537591907 Simplifying x = -0.537591907

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.162591907, -0.537591907}

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