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Simplifying 25u2 + 4 = 30u Reorder the terms: 4 + 25u2 = 30u Solving 4 + 25u2 = 30u Solving for variable 'u'. Reorder the terms: 4 + -30u + 25u2 = 30u + -30u Combine like terms: 30u + -30u = 0 4 + -30u + 25u2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.16 + -1.2u + u2 = 0 Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + -1.2u + -0.16 + u2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + -1.2u + u2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + -1.2u + u2 = 0 + -0.16 -1.2u + u2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 -1.2u + u2 = -0.16 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 = -0.16 + 0.36 Reorder the terms: 0.36 + -1.2u + u2 = -0.16 + 0.36 Combine like terms: -0.16 + 0.36 = 0.2 0.36 + -1.2u + u2 = 0.2 Factor a perfect square on the left side: (u + -0.6)(u + -0.6) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (u + -0.6) equal to 0.447213596 and -0.447213596.Subproblem 1
u + -0.6 = 0.447213596 Simplifying u + -0.6 = 0.447213596 Reorder the terms: -0.6 + u = 0.447213596 Solving -0.6 + u = 0.447213596 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 = 0.447213596 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + u = 0.447213596 + 0.6 u = 0.447213596 + 0.6 Combine like terms: 0.447213596 + 0.6 = 1.047213596 u = 1.047213596 Simplifying u = 1.047213596Subproblem 2
u + -0.6 = -0.447213596 Simplifying u + -0.6 = -0.447213596 Reorder the terms: -0.6 + u = -0.447213596 Solving -0.6 + u = -0.447213596 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 = -0.447213596 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + u = -0.447213596 + 0.6 u = -0.447213596 + 0.6 Combine like terms: -0.447213596 + 0.6 = 0.152786404 u = 0.152786404 Simplifying u = 0.152786404Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.047213596, 0.152786404}
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