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Simplifying 25u2 + -30u + -12 = 0 Reorder the terms: -12 + -30u + 25u2 = 0 Solving -12 + -30u + 25u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.48 + -1.2u + u2 = 0 Move the constant term to the right: Add '0.48' to each side of the equation. -0.48 + -1.2u + 0.48 + u2 = 0 + 0.48 Reorder the terms: -0.48 + 0.48 + -1.2u + u2 = 0 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + -1.2u + u2 = 0 + 0.48 -1.2u + u2 = 0 + 0.48 Combine like terms: 0 + 0.48 = 0.48 -1.2u + u2 = 0.48 The u term is -1.2u. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2u + 0.36 + u2 = 0.48 + 0.36 Reorder the terms: 0.36 + -1.2u + u2 = 0.48 + 0.36 Combine like terms: 0.48 + 0.36 = 0.84 0.36 + -1.2u + u2 = 0.84 Factor a perfect square on the left side: (u + -0.6)(u + -0.6) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (u + -0.6) equal to 0.916515139 and -0.916515139.Subproblem 1
u + -0.6 = 0.916515139 Simplifying u + -0.6 = 0.916515139 Reorder the terms: -0.6 + u = 0.916515139 Solving -0.6 + u = 0.916515139 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + u = 0.916515139 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + u = 0.916515139 + 0.6 u = 0.916515139 + 0.6 Combine like terms: 0.916515139 + 0.6 = 1.516515139 u = 1.516515139 Simplifying u = 1.516515139Subproblem 2
u + -0.6 = -0.916515139 Simplifying u + -0.6 = -0.916515139 Reorder the terms: -0.6 + u = -0.916515139 Solving -0.6 + u = -0.916515139 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + u = -0.916515139 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + u = -0.916515139 + 0.6 u = -0.916515139 + 0.6 Combine like terms: -0.916515139 + 0.6 = -0.316515139 u = -0.316515139 Simplifying u = -0.316515139Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.516515139, -0.316515139}
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