-9x^2+8x+5=0

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


Simplifying
-9x2 + 8x + 5 = 0

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

Solving
5 + 8x + -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'.
-0.5555555556 + -0.8888888889x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is -0.8888888889x.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889x + 0.1975308642 + x2 = 0.5555555556 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889x + x2 = 0.5555555556 + 0.1975308642

Combine like terms: 0.5555555556 + 0.1975308642 = 0.7530864198
0.1975308642 + -0.8888888889x + x2 = 0.7530864198

Factor a perfect square on the left side:
(x + -0.4444444445)(x + -0.4444444445) = 0.7530864198

Calculate the square root of the right side: 0.86780552

Break this problem into two subproblems by setting 
(x + -0.4444444445) equal to 0.86780552 and -0.86780552.

Subproblem 1

x + -0.4444444445 = 0.86780552 Simplifying x + -0.4444444445 = 0.86780552 Reorder the terms: -0.4444444445 + x = 0.86780552 Solving -0.4444444445 + x = 0.86780552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 0.86780552 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 0.86780552 + 0.4444444445 x = 0.86780552 + 0.4444444445 Combine like terms: 0.86780552 + 0.4444444445 = 1.3122499645 x = 1.3122499645 Simplifying x = 1.3122499645

Subproblem 2

x + -0.4444444445 = -0.86780552 Simplifying x + -0.4444444445 = -0.86780552 Reorder the terms: -0.4444444445 + x = -0.86780552 Solving -0.4444444445 + x = -0.86780552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -0.86780552 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -0.86780552 + 0.4444444445 x = -0.86780552 + 0.4444444445 Combine like terms: -0.86780552 + 0.4444444445 = -0.4233610755 x = -0.4233610755 Simplifying x = -0.4233610755

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.3122499645, -0.4233610755}

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