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