22x^2-11x-8=

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Solution for 22x^2-11x-8= equation:


Simplifying
22x2 + -11x + -8 = 0

Reorder the terms:
-8 + -11x + 22x2 = 0

Solving
-8 + -11x + 22x2 = 0

Solving for variable 'x'.

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

Divide each side by '22'.
-0.3636363636 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.3636363636' to each side of the equation.
-0.3636363636 + -0.5x + 0.3636363636 + x2 = 0 + 0.3636363636

Reorder the terms:
-0.3636363636 + 0.3636363636 + -0.5x + x2 = 0 + 0.3636363636

Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000
0.0000000000 + -0.5x + x2 = 0 + 0.3636363636
-0.5x + x2 = 0 + 0.3636363636

Combine like terms: 0 + 0.3636363636 = 0.3636363636
-0.5x + x2 = 0.3636363636

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.3636363636 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.3636363636 + 0.0625

Combine like terms: 0.3636363636 + 0.0625 = 0.4261363636
0.0625 + -0.5x + x2 = 0.4261363636

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.4261363636

Calculate the square root of the right side: 0.65279121

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.65279121 and -0.65279121.

Subproblem 1

x + -0.25 = 0.65279121 Simplifying x + -0.25 = 0.65279121 Reorder the terms: -0.25 + x = 0.65279121 Solving -0.25 + x = 0.65279121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.65279121 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.65279121 + 0.25 x = 0.65279121 + 0.25 Combine like terms: 0.65279121 + 0.25 = 0.90279121 x = 0.90279121 Simplifying x = 0.90279121

Subproblem 2

x + -0.25 = -0.65279121 Simplifying x + -0.25 = -0.65279121 Reorder the terms: -0.25 + x = -0.65279121 Solving -0.25 + x = -0.65279121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.65279121 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.65279121 + 0.25 x = -0.65279121 + 0.25 Combine like terms: -0.65279121 + 0.25 = -0.40279121 x = -0.40279121 Simplifying x = -0.40279121

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.90279121, -0.40279121}

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