9x^2-4x-22=0

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Solution for 9x^2-4x-22=0 equation:


Simplifying
9x2 + -4x + -22 = 0

Reorder the terms:
-22 + -4x + 9x2 = 0

Solving
-22 + -4x + 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'.
-2.444444444 + -0.4444444444x + x2 = 0

Move the constant term to the right:

Add '2.444444444' to each side of the equation.
-2.444444444 + -0.4444444444x + 2.444444444 + x2 = 0 + 2.444444444

Reorder the terms:
-2.444444444 + 2.444444444 + -0.4444444444x + x2 = 0 + 2.444444444

Combine like terms: -2.444444444 + 2.444444444 = 0.000000000
0.000000000 + -0.4444444444x + x2 = 0 + 2.444444444
-0.4444444444x + x2 = 0 + 2.444444444

Combine like terms: 0 + 2.444444444 = 2.444444444
-0.4444444444x + x2 = 2.444444444

The x term is -0.4444444444x.  Take half its coefficient (-0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
-0.4444444444x + 0.04938271604 + x2 = 2.444444444 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444x + x2 = 2.444444444 + 0.04938271604

Combine like terms: 2.444444444 + 0.04938271604 = 2.49382716004
0.04938271604 + -0.4444444444x + x2 = 2.49382716004

Factor a perfect square on the left side:
(x + -0.2222222222)(x + -0.2222222222) = 2.49382716004

Calculate the square root of the right side: 1.5791856

Break this problem into two subproblems by setting 
(x + -0.2222222222) equal to 1.5791856 and -1.5791856.

Subproblem 1

x + -0.2222222222 = 1.5791856 Simplifying x + -0.2222222222 = 1.5791856 Reorder the terms: -0.2222222222 + x = 1.5791856 Solving -0.2222222222 + x = 1.5791856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 1.5791856 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 1.5791856 + 0.2222222222 x = 1.5791856 + 0.2222222222 Combine like terms: 1.5791856 + 0.2222222222 = 1.8014078222 x = 1.8014078222 Simplifying x = 1.8014078222

Subproblem 2

x + -0.2222222222 = -1.5791856 Simplifying x + -0.2222222222 = -1.5791856 Reorder the terms: -0.2222222222 + x = -1.5791856 Solving -0.2222222222 + x = -1.5791856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -1.5791856 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -1.5791856 + 0.2222222222 x = -1.5791856 + 0.2222222222 Combine like terms: -1.5791856 + 0.2222222222 = -1.3569633778 x = -1.3569633778 Simplifying x = -1.3569633778

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.8014078222, -1.3569633778}

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