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Simplifying 20u2 + 65u + -600 = 0 Reorder the terms: -600 + 65u + 20u2 = 0 Solving -600 + 65u + 20u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '5'. 5(-120 + 13u + 4u2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-120 + 13u + 4u2)' equal to zero and attempt to solve: Simplifying -120 + 13u + 4u2 = 0 Solving -120 + 13u + 4u2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -30 + 3.25u + u2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 3.25u + 30 + u2 = 0 + 30 Reorder the terms: -30 + 30 + 3.25u + u2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 3.25u + u2 = 0 + 30 3.25u + u2 = 0 + 30 Combine like terms: 0 + 30 = 30 3.25u + u2 = 30 The u term is 3.25u. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25u + 2.640625 + u2 = 30 + 2.640625 Reorder the terms: 2.640625 + 3.25u + u2 = 30 + 2.640625 Combine like terms: 30 + 2.640625 = 32.640625 2.640625 + 3.25u + u2 = 32.640625 Factor a perfect square on the left side: (u + 1.625)(u + 1.625) = 32.640625 Calculate the square root of the right side: 5.713197441 Break this problem into two subproblems by setting (u + 1.625) equal to 5.713197441 and -5.713197441.Subproblem 1
u + 1.625 = 5.713197441 Simplifying u + 1.625 = 5.713197441 Reorder the terms: 1.625 + u = 5.713197441 Solving 1.625 + u = 5.713197441 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + u = 5.713197441 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + u = 5.713197441 + -1.625 u = 5.713197441 + -1.625 Combine like terms: 5.713197441 + -1.625 = 4.088197441 u = 4.088197441 Simplifying u = 4.088197441Subproblem 2
u + 1.625 = -5.713197441 Simplifying u + 1.625 = -5.713197441 Reorder the terms: 1.625 + u = -5.713197441 Solving 1.625 + u = -5.713197441 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + u = -5.713197441 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + u = -5.713197441 + -1.625 u = -5.713197441 + -1.625 Combine like terms: -5.713197441 + -1.625 = -7.338197441 u = -7.338197441 Simplifying u = -7.338197441Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.088197441, -7.338197441}Solution
u = {4.088197441, -7.338197441}
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