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Simplifying 9x2 + -6x + -11 = 0 Reorder the terms: -11 + -6x + 9x2 = 0 Solving -11 + -6x + 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 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + -0.6666666667x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + -0.6666666667x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + 1.222222222 -0.6666666667x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 -0.6666666667x + x2 = 1.222222222 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 1.222222222 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 1.222222222 + 0.1111111112 Combine like terms: 1.222222222 + 0.1111111112 = 1.3333333332 0.1111111112 + -0.6666666667x + x2 = 1.3333333332 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 1.3333333332 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 1.154700538 and -1.154700538.Subproblem 1
x + -0.3333333334 = 1.154700538 Simplifying x + -0.3333333334 = 1.154700538 Reorder the terms: -0.3333333334 + x = 1.154700538 Solving -0.3333333334 + x = 1.154700538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 1.154700538 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 1.154700538 + 0.3333333334 x = 1.154700538 + 0.3333333334 Combine like terms: 1.154700538 + 0.3333333334 = 1.4880338714 x = 1.4880338714 Simplifying x = 1.4880338714Subproblem 2
x + -0.3333333334 = -1.154700538 Simplifying x + -0.3333333334 = -1.154700538 Reorder the terms: -0.3333333334 + x = -1.154700538 Solving -0.3333333334 + x = -1.154700538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -1.154700538 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -1.154700538 + 0.3333333334 x = -1.154700538 + 0.3333333334 Combine like terms: -1.154700538 + 0.3333333334 = -0.8213672046 x = -0.8213672046 Simplifying x = -0.8213672046Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4880338714, -0.8213672046}
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