9x^2-4x-10=x-8

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Solution for 9x^2-4x-10=x-8 equation:


Simplifying
9x2 + -4x + -10 = x + -8

Reorder the terms:
-10 + -4x + 9x2 = x + -8

Reorder the terms:
-10 + -4x + 9x2 = -8 + x

Solving
-10 + -4x + 9x2 = -8 + x

Solving for variable 'x'.

Reorder the terms:
-10 + 8 + -4x + -1x + 9x2 = -8 + x + 8 + -1x

Combine like terms: -10 + 8 = -2
-2 + -4x + -1x + 9x2 = -8 + x + 8 + -1x

Combine like terms: -4x + -1x = -5x
-2 + -5x + 9x2 = -8 + x + 8 + -1x

Reorder the terms:
-2 + -5x + 9x2 = -8 + 8 + x + -1x

Combine like terms: -8 + 8 = 0
-2 + -5x + 9x2 = 0 + x + -1x
-2 + -5x + 9x2 = x + -1x

Combine like terms: x + -1x = 0
-2 + -5x + 9x2 = 0

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

Divide each side by '9'.
-0.2222222222 + -0.5555555556x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -0.5555555556x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -0.5555555556x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -0.5555555556x + x2 = 0 + 0.2222222222
-0.5555555556x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-0.5555555556x + x2 = 0.2222222222

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 = 0.2222222222 + 0.07716049384

Reorder the terms:
0.07716049384 + -0.5555555556x + x2 = 0.2222222222 + 0.07716049384

Combine like terms: 0.2222222222 + 0.07716049384 = 0.29938271604
0.07716049384 + -0.5555555556x + x2 = 0.29938271604

Factor a perfect square on the left side:
(x + -0.2777777778)(x + -0.2777777778) = 0.29938271604

Calculate the square root of the right side: 0.547158767

Break this problem into two subproblems by setting 
(x + -0.2777777778) equal to 0.547158767 and -0.547158767.

Subproblem 1

x + -0.2777777778 = 0.547158767 Simplifying x + -0.2777777778 = 0.547158767 Reorder the terms: -0.2777777778 + x = 0.547158767 Solving -0.2777777778 + x = 0.547158767 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 = 0.547158767 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 0.547158767 + 0.2777777778 x = 0.547158767 + 0.2777777778 Combine like terms: 0.547158767 + 0.2777777778 = 0.8249365448 x = 0.8249365448 Simplifying x = 0.8249365448

Subproblem 2

x + -0.2777777778 = -0.547158767 Simplifying x + -0.2777777778 = -0.547158767 Reorder the terms: -0.2777777778 + x = -0.547158767 Solving -0.2777777778 + x = -0.547158767 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 = -0.547158767 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -0.547158767 + 0.2777777778 x = -0.547158767 + 0.2777777778 Combine like terms: -0.547158767 + 0.2777777778 = -0.2693809892 x = -0.2693809892 Simplifying x = -0.2693809892

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8249365448, -0.2693809892}

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