9x^2+5x-8=0

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Solution for 9x^2+5x-8=0 equation:


Simplifying
9x2 + 5x + -8 = 0

Reorder the terms:
-8 + 5x + 9x2 = 0

Solving
-8 + 5x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.8888888889 + 0.5555555556x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + 0.5555555556x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + 0.5555555556x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + 0.5555555556x + x2 = 0 + 0.8888888889
0.5555555556x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
0.5555555556x + x2 = 0.8888888889

The x term is 0.5555555556x.  Take half its coefficient (0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
0.5555555556x + 0.07716049384 + x2 = 0.8888888889 + 0.07716049384

Reorder the terms:
0.07716049384 + 0.5555555556x + x2 = 0.8888888889 + 0.07716049384

Combine like terms: 0.8888888889 + 0.07716049384 = 0.96604938274
0.07716049384 + 0.5555555556x + x2 = 0.96604938274

Factor a perfect square on the left side:
(x + 0.2777777778)(x + 0.2777777778) = 0.96604938274

Calculate the square root of the right side: 0.982878112

Break this problem into two subproblems by setting 
(x + 0.2777777778) equal to 0.982878112 and -0.982878112.

Subproblem 1

x + 0.2777777778 = 0.982878112 Simplifying x + 0.2777777778 = 0.982878112 Reorder the terms: 0.2777777778 + x = 0.982878112 Solving 0.2777777778 + x = 0.982878112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 0.982878112 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 0.982878112 + -0.2777777778 x = 0.982878112 + -0.2777777778 Combine like terms: 0.982878112 + -0.2777777778 = 0.7051003342 x = 0.7051003342 Simplifying x = 0.7051003342

Subproblem 2

x + 0.2777777778 = -0.982878112 Simplifying x + 0.2777777778 = -0.982878112 Reorder the terms: 0.2777777778 + x = -0.982878112 Solving 0.2777777778 + x = -0.982878112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -0.982878112 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -0.982878112 + -0.2777777778 x = -0.982878112 + -0.2777777778 Combine like terms: -0.982878112 + -0.2777777778 = -1.2606558898 x = -1.2606558898 Simplifying x = -1.2606558898

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7051003342, -1.2606558898}

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