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Simplifying 9x2 = -22x + -12 Reorder the terms: 9x2 = -12 + -22x Solving 9x2 = -12 + -22x Solving for variable 'x'. Reorder the terms: 12 + 22x + 9x2 = -12 + -22x + 12 + 22x Reorder the terms: 12 + 22x + 9x2 = -12 + 12 + -22x + 22x Combine like terms: -12 + 12 = 0 12 + 22x + 9x2 = 0 + -22x + 22x 12 + 22x + 9x2 = -22x + 22x Combine like terms: -22x + 22x = 0 12 + 22x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.333333333 + 2.444444444x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 2.444444444x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 2.444444444x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 2.444444444x + x2 = 0 + -1.333333333 2.444444444x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 2.444444444x + x2 = -1.333333333 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 = -1.333333333 + 1.493827160 Reorder the terms: 1.493827160 + 2.444444444x + x2 = -1.333333333 + 1.493827160 Combine like terms: -1.333333333 + 1.493827160 = 0.160493827 1.493827160 + 2.444444444x + x2 = 0.160493827 Factor a perfect square on the left side: (x + 1.222222222)(x + 1.222222222) = 0.160493827 Calculate the square root of the right side: 0.400616808 Break this problem into two subproblems by setting (x + 1.222222222) equal to 0.400616808 and -0.400616808.Subproblem 1
x + 1.222222222 = 0.400616808 Simplifying x + 1.222222222 = 0.400616808 Reorder the terms: 1.222222222 + x = 0.400616808 Solving 1.222222222 + x = 0.400616808 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 = 0.400616808 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + x = 0.400616808 + -1.222222222 x = 0.400616808 + -1.222222222 Combine like terms: 0.400616808 + -1.222222222 = -0.821605414 x = -0.821605414 Simplifying x = -0.821605414Subproblem 2
x + 1.222222222 = -0.400616808 Simplifying x + 1.222222222 = -0.400616808 Reorder the terms: 1.222222222 + x = -0.400616808 Solving 1.222222222 + x = -0.400616808 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 = -0.400616808 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + x = -0.400616808 + -1.222222222 x = -0.400616808 + -1.222222222 Combine like terms: -0.400616808 + -1.222222222 = -1.62283903 x = -1.62283903 Simplifying x = -1.62283903Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.821605414, -1.62283903}
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