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Simplifying 9x2 + -12x + -36 = 38 Reorder the terms: -36 + -12x + 9x2 = 38 Solving -36 + -12x + 9x2 = 38 Solving for variable 'x'. Reorder the terms: -36 + -38 + -12x + 9x2 = 38 + -38 Combine like terms: -36 + -38 = -74 -74 + -12x + 9x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -74 + -12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -8.222222222 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '8.222222222' to each side of the equation. -8.222222222 + -1.333333333x + 8.222222222 + x2 = 0 + 8.222222222 Reorder the terms: -8.222222222 + 8.222222222 + -1.333333333x + x2 = 0 + 8.222222222 Combine like terms: -8.222222222 + 8.222222222 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + 8.222222222 -1.333333333x + x2 = 0 + 8.222222222 Combine like terms: 0 + 8.222222222 = 8.222222222 -1.333333333x + x2 = 8.222222222 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 = 8.222222222 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 8.222222222 + 0.4444444442 Combine like terms: 8.222222222 + 0.4444444442 = 8.6666666662 0.4444444442 + -1.333333333x + x2 = 8.6666666662 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 8.6666666662 Calculate the square root of the right side: 2.943920289 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 2.943920289 and -2.943920289.Subproblem 1
x + -0.6666666665 = 2.943920289 Simplifying x + -0.6666666665 = 2.943920289 Reorder the terms: -0.6666666665 + x = 2.943920289 Solving -0.6666666665 + x = 2.943920289 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 = 2.943920289 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 2.943920289 + 0.6666666665 x = 2.943920289 + 0.6666666665 Combine like terms: 2.943920289 + 0.6666666665 = 3.6105869555 x = 3.6105869555 Simplifying x = 3.6105869555Subproblem 2
x + -0.6666666665 = -2.943920289 Simplifying x + -0.6666666665 = -2.943920289 Reorder the terms: -0.6666666665 + x = -2.943920289 Solving -0.6666666665 + x = -2.943920289 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 = -2.943920289 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -2.943920289 + 0.6666666665 x = -2.943920289 + 0.6666666665 Combine like terms: -2.943920289 + 0.6666666665 = -2.2772536225 x = -2.2772536225 Simplifying x = -2.2772536225Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6105869555, -2.2772536225}
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