8x^2+9x-8=0

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


Simplifying
8x2 + 9x + -8 = 0

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

Solving
-8 + 9x + 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 + 1.125x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.125x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.125x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.125x + x2 = 0 + 1
1.125x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.125x + x2 = 1

The x term is 1.125x.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125x + 0.31640625 + x2 = 1 + 0.31640625

Reorder the terms:
0.31640625 + 1.125x + x2 = 1 + 0.31640625

Combine like terms: 1 + 0.31640625 = 1.31640625
0.31640625 + 1.125x + x2 = 1.31640625

Factor a perfect square on the left side:
(x + 0.5625)(x + 0.5625) = 1.31640625

Calculate the square root of the right side: 1.147347484

Break this problem into two subproblems by setting 
(x + 0.5625) equal to 1.147347484 and -1.147347484.

Subproblem 1

x + 0.5625 = 1.147347484 Simplifying x + 0.5625 = 1.147347484 Reorder the terms: 0.5625 + x = 1.147347484 Solving 0.5625 + x = 1.147347484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 1.147347484 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 1.147347484 + -0.5625 x = 1.147347484 + -0.5625 Combine like terms: 1.147347484 + -0.5625 = 0.584847484 x = 0.584847484 Simplifying x = 0.584847484

Subproblem 2

x + 0.5625 = -1.147347484 Simplifying x + 0.5625 = -1.147347484 Reorder the terms: 0.5625 + x = -1.147347484 Solving 0.5625 + x = -1.147347484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -1.147347484 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -1.147347484 + -0.5625 x = -1.147347484 + -0.5625 Combine like terms: -1.147347484 + -0.5625 = -1.709847484 x = -1.709847484 Simplifying x = -1.709847484

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.584847484, -1.709847484}

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