8x^2+13x-62=0

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Solution for 8x^2+13x-62=0 equation: 


Simplifying
8x2 + 13x + -62 = 0

Reorder the terms:
-62 + 13x + 8x2 = 0

Solving
-62 + 13x + 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'.
-7.75 + 1.625x + x2 = 0

Move the constant term to the right:

Add '7.75' to each side of the equation.
-7.75 + 1.625x + 7.75 + x2 = 0 + 7.75

Reorder the terms:
-7.75 + 7.75 + 1.625x + x2 = 0 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + 1.625x + x2 = 0 + 7.75
1.625x + x2 = 0 + 7.75

Combine like terms: 0 + 7.75 = 7.75
1.625x + x2 = 7.75

The x term is 1.625x.  Take half its coefficient (0.8125).
Square it (0.66015625) and add it to both sides.

Add '0.66015625' to each side of the equation.
1.625x + 0.66015625 + x2 = 7.75 + 0.66015625

Reorder the terms:
0.66015625 + 1.625x + x2 = 7.75 + 0.66015625

Combine like terms: 7.75 + 0.66015625 = 8.41015625
0.66015625 + 1.625x + x2 = 8.41015625

Factor a perfect square on the left side:
(x + 0.8125)(x + 0.8125) = 8.41015625

Calculate the square root of the right side: 2.90002694

Break this problem into two subproblems by setting 
(x + 0.8125) equal to 2.90002694 and -2.90002694.


Subproblem 1
x + 0.8125 = 2.90002694

Simplifying
x + 0.8125 = 2.90002694

Reorder the terms:
0.8125 + x = 2.90002694

Solving
0.8125 + x = 2.90002694

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.8125' to each side of the equation.
0.8125 + -0.8125 + x = 2.90002694 + -0.8125

Combine like terms: 0.8125 + -0.8125 = 0.0000
0.0000 + x = 2.90002694 + -0.8125
x = 2.90002694 + -0.8125

Combine like terms: 2.90002694 + -0.8125 = 2.08752694
x = 2.08752694

Simplifying
x = 2.08752694


Subproblem 2
x + 0.8125 = -2.90002694

Simplifying
x + 0.8125 = -2.90002694

Reorder the terms:
0.8125 + x = -2.90002694

Solving
0.8125 + x = -2.90002694

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.8125' to each side of the equation.
0.8125 + -0.8125 + x = -2.90002694 + -0.8125

Combine like terms: 0.8125 + -0.8125 = 0.0000
0.0000 + x = -2.90002694 + -0.8125
x = -2.90002694 + -0.8125

Combine like terms: -2.90002694 + -0.8125 = -3.71252694
x = -3.71252694

Simplifying
x = -3.71252694


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.08752694, -3.71252694}

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