9x^2-22x-4=0

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


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

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

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

Move the constant term to the right:

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

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

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -2.444444444x + x2 = 0 + 0.4444444444
-2.444444444x + x2 = 0 + 0.4444444444

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

The x term is -2.444444444x.  Take half its coefficient (-1.222222222).
Square it (1.493827160) and add it to both sides.

Add '1.493827160' to each side of the equation.
-2.444444444x + 1.493827160 + x2 = 0.4444444444 + 1.493827160

Reorder the terms:
1.493827160 + -2.444444444x + x2 = 0.4444444444 + 1.493827160

Combine like terms: 0.4444444444 + 1.493827160 = 1.9382716044
1.493827160 + -2.444444444x + x2 = 1.9382716044

Factor a perfect square on the left side:
(x + -1.222222222)(x + -1.222222222) = 1.9382716044

Calculate the square root of the right side: 1.392218232

Break this problem into two subproblems by setting 
(x + -1.222222222) equal to 1.392218232 and -1.392218232.

Subproblem 1

x + -1.222222222 = 1.392218232 Simplifying x + -1.222222222 = 1.392218232 Reorder the terms: -1.222222222 + x = 1.392218232 Solving -1.222222222 + x = 1.392218232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.222222222' to each side of the equation. -1.222222222 + 1.222222222 + x = 1.392218232 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + x = 1.392218232 + 1.222222222 x = 1.392218232 + 1.222222222 Combine like terms: 1.392218232 + 1.222222222 = 2.614440454 x = 2.614440454 Simplifying x = 2.614440454

Subproblem 2

x + -1.222222222 = -1.392218232 Simplifying x + -1.222222222 = -1.392218232 Reorder the terms: -1.222222222 + x = -1.392218232 Solving -1.222222222 + x = -1.392218232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.222222222' to each side of the equation. -1.222222222 + 1.222222222 + x = -1.392218232 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + x = -1.392218232 + 1.222222222 x = -1.392218232 + 1.222222222 Combine like terms: -1.392218232 + 1.222222222 = -0.16999601 x = -0.16999601 Simplifying x = -0.16999601

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.614440454, -0.16999601}

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