7x^2+5x-8=0

Solution for 7x^2+5x-8=0 equation:

Simplifying
7x2 + 5x + -8 = 0

Reorder the terms:
-8 + 5x + 7x2 = 0

Solving
-8 + 5x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-1.142857143 + 0.7142857143x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + 0.7142857143x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + 0.7142857143x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + 0.7142857143x + x2 = 0 + 1.142857143
0.7142857143x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
0.7142857143x + x2 = 1.142857143

The x term is 0.7142857143x.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143x + 0.1275510204 + x2 = 1.142857143 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143x + x2 = 1.142857143 + 0.1275510204

Combine like terms: 1.142857143 + 0.1275510204 = 1.2704081634
0.1275510204 + 0.7142857143x + x2 = 1.2704081634

Factor a perfect square on the left side:
(x + 0.3571428572)(x + 0.3571428572) = 1.2704081634

Calculate the square root of the right side: 1.127123846

Break this problem into two subproblems by setting 
(x + 0.3571428572) equal to 1.127123846 and -1.127123846.

Subproblem 1
x + 0.3571428572 = 1.127123846

Simplifying
x + 0.3571428572 = 1.127123846

Reorder the terms:
0.3571428572 + x = 1.127123846

Solving
0.3571428572 + x = 1.127123846

Solving for variable 'x'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + x = 1.127123846 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + x = 1.127123846 + -0.3571428572
x = 1.127123846 + -0.3571428572

Combine like terms: 1.127123846 + -0.3571428572 = 0.7699809888
x = 0.7699809888

Simplifying
x = 0.7699809888

Subproblem 2
x + 0.3571428572 = -1.127123846

Simplifying
x + 0.3571428572 = -1.127123846

Reorder the terms:
0.3571428572 + x = -1.127123846

Solving
0.3571428572 + x = -1.127123846

Solving for variable 'x'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + x = -1.127123846 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + x = -1.127123846 + -0.3571428572
x = -1.127123846 + -0.3571428572

Combine like terms: -1.127123846 + -0.3571428572 = -1.4842667032
x = -1.4842667032

Simplifying
x = -1.4842667032

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7699809888, -1.4842667032}