8x^2+25x+13=0

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Solution for 8x^2+25x+13=0 equation:


Simplifying
8x2 + 25x + 13 = 0

Reorder the terms:
13 + 25x + 8x2 = 0

Solving
13 + 25x + 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'.
1.625 + 3.125x + x2 = 0

Move the constant term to the right:

Add '-1.625' to each side of the equation.
1.625 + 3.125x + -1.625 + x2 = 0 + -1.625

Reorder the terms:
1.625 + -1.625 + 3.125x + x2 = 0 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + 3.125x + x2 = 0 + -1.625
3.125x + x2 = 0 + -1.625

Combine like terms: 0 + -1.625 = -1.625
3.125x + x2 = -1.625

The x term is 3.125x.  Take half its coefficient (1.5625).
Square it (2.44140625) and add it to both sides.

Add '2.44140625' to each side of the equation.
3.125x + 2.44140625 + x2 = -1.625 + 2.44140625

Reorder the terms:
2.44140625 + 3.125x + x2 = -1.625 + 2.44140625

Combine like terms: -1.625 + 2.44140625 = 0.81640625
2.44140625 + 3.125x + x2 = 0.81640625

Factor a perfect square on the left side:
(x + 1.5625)(x + 1.5625) = 0.81640625

Calculate the square root of the right side: 0.903552018

Break this problem into two subproblems by setting 
(x + 1.5625) equal to 0.903552018 and -0.903552018.

Subproblem 1

x + 1.5625 = 0.903552018 Simplifying x + 1.5625 = 0.903552018 Reorder the terms: 1.5625 + x = 0.903552018 Solving 1.5625 + x = 0.903552018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = 0.903552018 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = 0.903552018 + -1.5625 x = 0.903552018 + -1.5625 Combine like terms: 0.903552018 + -1.5625 = -0.658947982 x = -0.658947982 Simplifying x = -0.658947982

Subproblem 2

x + 1.5625 = -0.903552018 Simplifying x + 1.5625 = -0.903552018 Reorder the terms: 1.5625 + x = -0.903552018 Solving 1.5625 + x = -0.903552018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + x = -0.903552018 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + x = -0.903552018 + -1.5625 x = -0.903552018 + -1.5625 Combine like terms: -0.903552018 + -1.5625 = -2.466052018 x = -2.466052018 Simplifying x = -2.466052018

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.658947982, -2.466052018}

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