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Simplifying u(u + -15) = 180 Reorder the terms: u(-15 + u) = 180 (-15 * u + u * u) = 180 (-15u + u2) = 180 Solving -15u + u2 = 180 Solving for variable 'u'. Reorder the terms: -180 + -15u + u2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -15u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -15u + 180 + u2 = 0 + 180 Reorder the terms: -180 + 180 + -15u + u2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -15u + u2 = 0 + 180 -15u + u2 = 0 + 180 Combine like terms: 0 + 180 = 180 -15u + u2 = 180 The u term is -15u. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15u + 56.25 + u2 = 180 + 56.25 Reorder the terms: 56.25 + -15u + u2 = 180 + 56.25 Combine like terms: 180 + 56.25 = 236.25 56.25 + -15u + u2 = 236.25 Factor a perfect square on the left side: (u + -7.5)(u + -7.5) = 236.25 Calculate the square root of the right side: 15.370426149 Break this problem into two subproblems by setting (u + -7.5) equal to 15.370426149 and -15.370426149.Subproblem 1
u + -7.5 = 15.370426149 Simplifying u + -7.5 = 15.370426149 Reorder the terms: -7.5 + u = 15.370426149 Solving -7.5 + u = 15.370426149 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + u = 15.370426149 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + u = 15.370426149 + 7.5 u = 15.370426149 + 7.5 Combine like terms: 15.370426149 + 7.5 = 22.870426149 u = 22.870426149 Simplifying u = 22.870426149Subproblem 2
u + -7.5 = -15.370426149 Simplifying u + -7.5 = -15.370426149 Reorder the terms: -7.5 + u = -15.370426149 Solving -7.5 + u = -15.370426149 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + u = -15.370426149 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + u = -15.370426149 + 7.5 u = -15.370426149 + 7.5 Combine like terms: -15.370426149 + 7.5 = -7.870426149 u = -7.870426149 Simplifying u = -7.870426149Solution
The solution to the problem is based on the solutions from the subproblems. u = {22.870426149, -7.870426149}
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