7x^2+9x-8=0

Solution for 7x^2+9x-8=0 equation:

Simplifying
7x2 + 9x + -8 = 0

Reorder the terms:
-8 + 9x + 7x2 = 0

Solving
-8 + 9x + 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 + 1.285714286x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.285714286x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + 1.285714286x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + 1.285714286x + x2 = 0 + 1.142857143
1.285714286x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
1.285714286x + x2 = 1.142857143

The x term is 1.285714286x.  Take half its coefficient (0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
1.285714286x + 0.4132653063 + x2 = 1.142857143 + 0.4132653063

Reorder the terms:
0.4132653063 + 1.285714286x + x2 = 1.142857143 + 0.4132653063

Combine like terms: 1.142857143 + 0.4132653063 = 1.5561224493
0.4132653063 + 1.285714286x + x2 = 1.5561224493

Factor a perfect square on the left side:
(x + 0.642857143)(x + 0.642857143) = 1.5561224493

Calculate the square root of the right side: 1.247446371

Break this problem into two subproblems by setting 
(x + 0.642857143) equal to 1.247446371 and -1.247446371.

Subproblem 1
x + 0.642857143 = 1.247446371

Simplifying
x + 0.642857143 = 1.247446371

Reorder the terms:
0.642857143 + x = 1.247446371

Solving
0.642857143 + x = 1.247446371

Solving for variable 'x'.

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

Add '-0.642857143' to each side of the equation.
0.642857143 + -0.642857143 + x = 1.247446371 + -0.642857143

Combine like terms: 0.642857143 + -0.642857143 = 0.000000000
0.000000000 + x = 1.247446371 + -0.642857143
x = 1.247446371 + -0.642857143

Combine like terms: 1.247446371 + -0.642857143 = 0.604589228
x = 0.604589228

Simplifying
x = 0.604589228

Subproblem 2
x + 0.642857143 = -1.247446371

Simplifying
x + 0.642857143 = -1.247446371

Reorder the terms:
0.642857143 + x = -1.247446371

Solving
0.642857143 + x = -1.247446371

Solving for variable 'x'.

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

Add '-0.642857143' to each side of the equation.
0.642857143 + -0.642857143 + x = -1.247446371 + -0.642857143

Combine like terms: 0.642857143 + -0.642857143 = 0.000000000
0.000000000 + x = -1.247446371 + -0.642857143
x = -1.247446371 + -0.642857143

Combine like terms: -1.247446371 + -0.642857143 = -1.890303514
x = -1.890303514

Simplifying
x = -1.890303514

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.604589228, -1.890303514}