8x^2+2x-5=0

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


Simplifying
8x2 + 2x + -5 = 0

Reorder the terms:
-5 + 2x + 8x2 = 0

Solving
-5 + 2x + 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 + 0.25x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 0.25x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 0.25x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 0.25x + x2 = 0 + 0.625
0.25x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
0.25x + x2 = 0.625

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 0.625 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 0.625 + 0.015625

Combine like terms: 0.625 + 0.015625 = 0.640625
0.015625 + 0.25x + x2 = 0.640625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.80039053 and -0.80039053.

Subproblem 1

x + 0.125 = 0.80039053 Simplifying x + 0.125 = 0.80039053 Reorder the terms: 0.125 + x = 0.80039053 Solving 0.125 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.80039053 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.80039053 + -0.125 x = 0.80039053 + -0.125 Combine like terms: 0.80039053 + -0.125 = 0.67539053 x = 0.67539053 Simplifying x = 0.67539053

Subproblem 2

x + 0.125 = -0.80039053 Simplifying x + 0.125 = -0.80039053 Reorder the terms: 0.125 + x = -0.80039053 Solving 0.125 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.80039053 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.80039053 + -0.125 x = -0.80039053 + -0.125 Combine like terms: -0.80039053 + -0.125 = -0.92539053 x = -0.92539053 Simplifying x = -0.92539053

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.67539053, -0.92539053}

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