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Simplifying 2u2 + -3u = 79 Reorder the terms: -3u + 2u2 = 79 Solving -3u + 2u2 = 79 Solving for variable 'u'. Reorder the terms: -79 + -3u + 2u2 = 79 + -79 Combine like terms: 79 + -79 = 0 -79 + -3u + 2u2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -39.5 + -1.5u + u2 = 0 Move the constant term to the right: Add '39.5' to each side of the equation. -39.5 + -1.5u + 39.5 + u2 = 0 + 39.5 Reorder the terms: -39.5 + 39.5 + -1.5u + u2 = 0 + 39.5 Combine like terms: -39.5 + 39.5 = 0.0 0.0 + -1.5u + u2 = 0 + 39.5 -1.5u + u2 = 0 + 39.5 Combine like terms: 0 + 39.5 = 39.5 -1.5u + u2 = 39.5 The u term is -1.5u. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5u + 0.5625 + u2 = 39.5 + 0.5625 Reorder the terms: 0.5625 + -1.5u + u2 = 39.5 + 0.5625 Combine like terms: 39.5 + 0.5625 = 40.0625 0.5625 + -1.5u + u2 = 40.0625 Factor a perfect square on the left side: (u + -0.75)(u + -0.75) = 40.0625 Calculate the square root of the right side: 6.329494451 Break this problem into two subproblems by setting (u + -0.75) equal to 6.329494451 and -6.329494451.Subproblem 1
u + -0.75 = 6.329494451 Simplifying u + -0.75 = 6.329494451 Reorder the terms: -0.75 + u = 6.329494451 Solving -0.75 + u = 6.329494451 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + u = 6.329494451 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + u = 6.329494451 + 0.75 u = 6.329494451 + 0.75 Combine like terms: 6.329494451 + 0.75 = 7.079494451 u = 7.079494451 Simplifying u = 7.079494451Subproblem 2
u + -0.75 = -6.329494451 Simplifying u + -0.75 = -6.329494451 Reorder the terms: -0.75 + u = -6.329494451 Solving -0.75 + u = -6.329494451 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + u = -6.329494451 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + u = -6.329494451 + 0.75 u = -6.329494451 + 0.75 Combine like terms: -6.329494451 + 0.75 = -5.579494451 u = -5.579494451 Simplifying u = -5.579494451Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.079494451, -5.579494451}
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