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Simplifying 9x2 + -12x = 71 Reorder the terms: -12x + 9x2 = 71 Solving -12x + 9x2 = 71 Solving for variable 'x'. Reorder the terms: -71 + -12x + 9x2 = 71 + -71 Combine like terms: 71 + -71 = 0 -71 + -12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -7.888888889 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '7.888888889' to each side of the equation. -7.888888889 + -1.333333333x + 7.888888889 + x2 = 0 + 7.888888889 Reorder the terms: -7.888888889 + 7.888888889 + -1.333333333x + x2 = 0 + 7.888888889 Combine like terms: -7.888888889 + 7.888888889 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + 7.888888889 -1.333333333x + x2 = 0 + 7.888888889 Combine like terms: 0 + 7.888888889 = 7.888888889 -1.333333333x + x2 = 7.888888889 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 7.888888889 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 7.888888889 + 0.4444444442 Combine like terms: 7.888888889 + 0.4444444442 = 8.3333333332 0.4444444442 + -1.333333333x + x2 = 8.3333333332 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 8.3333333332 Calculate the square root of the right side: 2.886751346 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 2.886751346 and -2.886751346.Subproblem 1
x + -0.6666666665 = 2.886751346 Simplifying x + -0.6666666665 = 2.886751346 Reorder the terms: -0.6666666665 + x = 2.886751346 Solving -0.6666666665 + x = 2.886751346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 2.886751346 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 2.886751346 + 0.6666666665 x = 2.886751346 + 0.6666666665 Combine like terms: 2.886751346 + 0.6666666665 = 3.5534180125 x = 3.5534180125 Simplifying x = 3.5534180125Subproblem 2
x + -0.6666666665 = -2.886751346 Simplifying x + -0.6666666665 = -2.886751346 Reorder the terms: -0.6666666665 + x = -2.886751346 Solving -0.6666666665 + x = -2.886751346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -2.886751346 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -2.886751346 + 0.6666666665 x = -2.886751346 + 0.6666666665 Combine like terms: -2.886751346 + 0.6666666665 = -2.2200846795 x = -2.2200846795 Simplifying x = -2.2200846795Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5534180125, -2.2200846795}
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