(9x-11)(9x-11)=99

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Solution for (9x-11)(9x-11)=99 equation:


Simplifying
(9x + -11)(9x + -11) = 99

Reorder the terms:
(-11 + 9x)(9x + -11) = 99

Reorder the terms:
(-11 + 9x)(-11 + 9x) = 99

Multiply (-11 + 9x) * (-11 + 9x)
(-11(-11 + 9x) + 9x * (-11 + 9x)) = 99
((-11 * -11 + 9x * -11) + 9x * (-11 + 9x)) = 99
((121 + -99x) + 9x * (-11 + 9x)) = 99
(121 + -99x + (-11 * 9x + 9x * 9x)) = 99
(121 + -99x + (-99x + 81x2)) = 99

Combine like terms: -99x + -99x = -198x
(121 + -198x + 81x2) = 99

Solving
121 + -198x + 81x2 = 99

Solving for variable 'x'.

Reorder the terms:
121 + -99 + -198x + 81x2 = 99 + -99

Combine like terms: 121 + -99 = 22
22 + -198x + 81x2 = 99 + -99

Combine like terms: 99 + -99 = 0
22 + -198x + 81x2 = 0

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

Divide each side by '81'.
0.2716049383 + -2.444444444x + x2 = 0

Move the constant term to the right:

Add '-0.2716049383' to each side of the equation.
0.2716049383 + -2.444444444x + -0.2716049383 + x2 = 0 + -0.2716049383

Reorder the terms:
0.2716049383 + -0.2716049383 + -2.444444444x + x2 = 0 + -0.2716049383

Combine like terms: 0.2716049383 + -0.2716049383 = 0.0000000000
0.0000000000 + -2.444444444x + x2 = 0 + -0.2716049383
-2.444444444x + x2 = 0 + -0.2716049383

Combine like terms: 0 + -0.2716049383 = -0.2716049383
-2.444444444x + x2 = -0.2716049383

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 = -0.2716049383 + 1.493827160

Reorder the terms:
1.493827160 + -2.444444444x + x2 = -0.2716049383 + 1.493827160

Combine like terms: -0.2716049383 + 1.493827160 = 1.2222222217
1.493827160 + -2.444444444x + x2 = 1.2222222217

Factor a perfect square on the left side:
(x + -1.222222222)(x + -1.222222222) = 1.2222222217

Calculate the square root of the right side: 1.105541597

Break this problem into two subproblems by setting 
(x + -1.222222222) equal to 1.105541597 and -1.105541597.

Subproblem 1

x + -1.222222222 = 1.105541597 Simplifying x + -1.222222222 = 1.105541597 Reorder the terms: -1.222222222 + x = 1.105541597 Solving -1.222222222 + x = 1.105541597 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 = 1.105541597 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + x = 1.105541597 + 1.222222222 x = 1.105541597 + 1.222222222 Combine like terms: 1.105541597 + 1.222222222 = 2.327763819 x = 2.327763819 Simplifying x = 2.327763819

Subproblem 2

x + -1.222222222 = -1.105541597 Simplifying x + -1.222222222 = -1.105541597 Reorder the terms: -1.222222222 + x = -1.105541597 Solving -1.222222222 + x = -1.105541597 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 = -1.105541597 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + x = -1.105541597 + 1.222222222 x = -1.105541597 + 1.222222222 Combine like terms: -1.105541597 + 1.222222222 = 0.116680625 x = 0.116680625 Simplifying x = 0.116680625

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.327763819, 0.116680625}

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