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Simplifying 4u2 + -10u + -15 = 0 Reorder the terms: -15 + -10u + 4u2 = 0 Solving -15 + -10u + 4u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -2.5u + u2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -2.5u + 3.75 + u2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -2.5u + u2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -2.5u + u2 = 0 + 3.75 -2.5u + u2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -2.5u + u2 = 3.75 The u term is -2.5u. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5u + 1.5625 + u2 = 3.75 + 1.5625 Reorder the terms: 1.5625 + -2.5u + u2 = 3.75 + 1.5625 Combine like terms: 3.75 + 1.5625 = 5.3125 1.5625 + -2.5u + u2 = 5.3125 Factor a perfect square on the left side: (u + -1.25)(u + -1.25) = 5.3125 Calculate the square root of the right side: 2.304886114 Break this problem into two subproblems by setting (u + -1.25) equal to 2.304886114 and -2.304886114.Subproblem 1
u + -1.25 = 2.304886114 Simplifying u + -1.25 = 2.304886114 Reorder the terms: -1.25 + u = 2.304886114 Solving -1.25 + u = 2.304886114 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + u = 2.304886114 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + u = 2.304886114 + 1.25 u = 2.304886114 + 1.25 Combine like terms: 2.304886114 + 1.25 = 3.554886114 u = 3.554886114 Simplifying u = 3.554886114Subproblem 2
u + -1.25 = -2.304886114 Simplifying u + -1.25 = -2.304886114 Reorder the terms: -1.25 + u = -2.304886114 Solving -1.25 + u = -2.304886114 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + u = -2.304886114 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + u = -2.304886114 + 1.25 u = -2.304886114 + 1.25 Combine like terms: -2.304886114 + 1.25 = -1.054886114 u = -1.054886114 Simplifying u = -1.054886114Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.554886114, -1.054886114}
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