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Simplifying 3x2 + 40x + -99 = 0 Reorder the terms: -99 + 40x + 3x2 = 0 Solving -99 + 40x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -33 + 13.33333333x + x2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + 13.33333333x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 13.33333333x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 13.33333333x + x2 = 0 + 33 13.33333333x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 13.33333333x + x2 = 33 The x term is 13.33333333x. Take half its coefficient (6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. 13.33333333x + 44.44444442 + x2 = 33 + 44.44444442 Reorder the terms: 44.44444442 + 13.33333333x + x2 = 33 + 44.44444442 Combine like terms: 33 + 44.44444442 = 77.44444442 44.44444442 + 13.33333333x + x2 = 77.44444442 Factor a perfect square on the left side: (x + 6.666666665)(x + 6.666666665) = 77.44444442 Calculate the square root of the right side: 8.80025252 Break this problem into two subproblems by setting (x + 6.666666665) equal to 8.80025252 and -8.80025252.Subproblem 1
x + 6.666666665 = 8.80025252 Simplifying x + 6.666666665 = 8.80025252 Reorder the terms: 6.666666665 + x = 8.80025252 Solving 6.666666665 + x = 8.80025252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.666666665' to each side of the equation. 6.666666665 + -6.666666665 + x = 8.80025252 + -6.666666665 Combine like terms: 6.666666665 + -6.666666665 = 0.000000000 0.000000000 + x = 8.80025252 + -6.666666665 x = 8.80025252 + -6.666666665 Combine like terms: 8.80025252 + -6.666666665 = 2.133585855 x = 2.133585855 Simplifying x = 2.133585855Subproblem 2
x + 6.666666665 = -8.80025252 Simplifying x + 6.666666665 = -8.80025252 Reorder the terms: 6.666666665 + x = -8.80025252 Solving 6.666666665 + x = -8.80025252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.666666665' to each side of the equation. 6.666666665 + -6.666666665 + x = -8.80025252 + -6.666666665 Combine like terms: 6.666666665 + -6.666666665 = 0.000000000 0.000000000 + x = -8.80025252 + -6.666666665 x = -8.80025252 + -6.666666665 Combine like terms: -8.80025252 + -6.666666665 = -15.466919185 x = -15.466919185 Simplifying x = -15.466919185Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.133585855, -15.466919185}
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