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

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


Simplifying
0 = -9x2 + 5x + 5

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

Solving
0 = 5 + 5x + -9x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -5x + 9x2 = 5 + 5x + -9x2 + -5 + -5x + 9x2

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

Combine like terms: 5 + -5 = 0
-5 + -5x + 9x2 = 0 + 5x + -5x + -9x2 + 9x2
-5 + -5x + 9x2 = 5x + -5x + -9x2 + 9x2

Combine like terms: 5x + -5x = 0
-5 + -5x + 9x2 = 0 + -9x2 + 9x2
-5 + -5x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-5 + -5x + 9x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

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 = 0.5555555556 + 0.07716049384

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

Combine like terms: 0.5555555556 + 0.07716049384 = 0.63271604944
0.07716049384 + -0.5555555556x + x2 = 0.63271604944

Factor a perfect square on the left side:
(x + -0.2777777778)(x + -0.2777777778) = 0.63271604944

Calculate the square root of the right side: 0.795434504

Break this problem into two subproblems by setting 
(x + -0.2777777778) equal to 0.795434504 and -0.795434504.

Subproblem 1

x + -0.2777777778 = 0.795434504 Simplifying x + -0.2777777778 = 0.795434504 Reorder the terms: -0.2777777778 + x = 0.795434504 Solving -0.2777777778 + x = 0.795434504 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 = 0.795434504 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 0.795434504 + 0.2777777778 x = 0.795434504 + 0.2777777778 Combine like terms: 0.795434504 + 0.2777777778 = 1.0732122818 x = 1.0732122818 Simplifying x = 1.0732122818

Subproblem 2

x + -0.2777777778 = -0.795434504 Simplifying x + -0.2777777778 = -0.795434504 Reorder the terms: -0.2777777778 + x = -0.795434504 Solving -0.2777777778 + x = -0.795434504 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 = -0.795434504 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -0.795434504 + 0.2777777778 x = -0.795434504 + 0.2777777778 Combine like terms: -0.795434504 + 0.2777777778 = -0.5176567262 x = -0.5176567262 Simplifying x = -0.5176567262

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.0732122818, -0.5176567262}

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