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Simplifying 9x2 + -9x + -11 = 0 Reorder the terms: -11 + -9x + 9x2 = 0 Solving -11 + -9x + 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'. -1.222222222 + -1x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + -1x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + -1x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + -1x + x2 = 0 + 1.222222222 -1x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 -1x + x2 = 1.222222222 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.222222222 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.222222222 + 0.25 Combine like terms: 1.222222222 + 0.25 = 1.472222222 0.25 + -1x + x2 = 1.472222222 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.472222222 Calculate the square root of the right side: 1.213351648 Break this problem into two subproblems by setting (x + -0.5) equal to 1.213351648 and -1.213351648.Subproblem 1
x + -0.5 = 1.213351648 Simplifying x + -0.5 = 1.213351648 Reorder the terms: -0.5 + x = 1.213351648 Solving -0.5 + x = 1.213351648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.213351648 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.213351648 + 0.5 x = 1.213351648 + 0.5 Combine like terms: 1.213351648 + 0.5 = 1.713351648 x = 1.713351648 Simplifying x = 1.713351648Subproblem 2
x + -0.5 = -1.213351648 Simplifying x + -0.5 = -1.213351648 Reorder the terms: -0.5 + x = -1.213351648 Solving -0.5 + x = -1.213351648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.213351648 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.213351648 + 0.5 x = -1.213351648 + 0.5 Combine like terms: -1.213351648 + 0.5 = -0.713351648 x = -0.713351648 Simplifying x = -0.713351648Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.713351648, -0.713351648}
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