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Simplifying 15u2 + -14u = 48 Reorder the terms: -14u + 15u2 = 48 Solving -14u + 15u2 = 48 Solving for variable 'u'. Reorder the terms: -48 + -14u + 15u2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -14u + 15u2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -3.2 + -0.9333333333u + u2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -0.9333333333u + 3.2 + u2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -0.9333333333u + u2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -0.9333333333u + u2 = 0 + 3.2 -0.9333333333u + u2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -0.9333333333u + u2 = 3.2 The u term is -0.9333333333u. Take half its coefficient (-0.4666666667). Square it (0.2177777778) and add it to both sides. Add '0.2177777778' to each side of the equation. -0.9333333333u + 0.2177777778 + u2 = 3.2 + 0.2177777778 Reorder the terms: 0.2177777778 + -0.9333333333u + u2 = 3.2 + 0.2177777778 Combine like terms: 3.2 + 0.2177777778 = 3.4177777778 0.2177777778 + -0.9333333333u + u2 = 3.4177777778 Factor a perfect square on the left side: (u + -0.4666666667)(u + -0.4666666667) = 3.4177777778 Calculate the square root of the right side: 1.848723283 Break this problem into two subproblems by setting (u + -0.4666666667) equal to 1.848723283 and -1.848723283.Subproblem 1
u + -0.4666666667 = 1.848723283 Simplifying u + -0.4666666667 = 1.848723283 Reorder the terms: -0.4666666667 + u = 1.848723283 Solving -0.4666666667 + u = 1.848723283 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.4666666667' to each side of the equation. -0.4666666667 + 0.4666666667 + u = 1.848723283 + 0.4666666667 Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000 0.0000000000 + u = 1.848723283 + 0.4666666667 u = 1.848723283 + 0.4666666667 Combine like terms: 1.848723283 + 0.4666666667 = 2.3153899497 u = 2.3153899497 Simplifying u = 2.3153899497Subproblem 2
u + -0.4666666667 = -1.848723283 Simplifying u + -0.4666666667 = -1.848723283 Reorder the terms: -0.4666666667 + u = -1.848723283 Solving -0.4666666667 + u = -1.848723283 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.4666666667' to each side of the equation. -0.4666666667 + 0.4666666667 + u = -1.848723283 + 0.4666666667 Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000 0.0000000000 + u = -1.848723283 + 0.4666666667 u = -1.848723283 + 0.4666666667 Combine like terms: -1.848723283 + 0.4666666667 = -1.3820566163 u = -1.3820566163 Simplifying u = -1.3820566163Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.3153899497, -1.3820566163}
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