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Simplifying -4u2 + -5u + 10 = 3 Reorder the terms: 10 + -5u + -4u2 = 3 Solving 10 + -5u + -4u2 = 3 Solving for variable 'u'. Reorder the terms: 10 + -3 + -5u + -4u2 = 3 + -3 Combine like terms: 10 + -3 = 7 7 + -5u + -4u2 = 3 + -3 Combine like terms: 3 + -3 = 0 7 + -5u + -4u2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + 1.25u + u2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 1.25u + 1.75 + u2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 1.25u + u2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 1.25u + u2 = 0 + 1.75 1.25u + u2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 1.25u + u2 = 1.75 The u term is 1.25u. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25u + 0.390625 + u2 = 1.75 + 0.390625 Reorder the terms: 0.390625 + 1.25u + u2 = 1.75 + 0.390625 Combine like terms: 1.75 + 0.390625 = 2.140625 0.390625 + 1.25u + u2 = 2.140625 Factor a perfect square on the left side: (u + 0.625)(u + 0.625) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (u + 0.625) equal to 1.463087489 and -1.463087489.Subproblem 1
u + 0.625 = 1.463087489 Simplifying u + 0.625 = 1.463087489 Reorder the terms: 0.625 + u = 1.463087489 Solving 0.625 + u = 1.463087489 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + u = 1.463087489 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + u = 1.463087489 + -0.625 u = 1.463087489 + -0.625 Combine like terms: 1.463087489 + -0.625 = 0.838087489 u = 0.838087489 Simplifying u = 0.838087489Subproblem 2
u + 0.625 = -1.463087489 Simplifying u + 0.625 = -1.463087489 Reorder the terms: 0.625 + u = -1.463087489 Solving 0.625 + u = -1.463087489 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + u = -1.463087489 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + u = -1.463087489 + -0.625 u = -1.463087489 + -0.625 Combine like terms: -1.463087489 + -0.625 = -2.088087489 u = -2.088087489 Simplifying u = -2.088087489Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.838087489, -2.088087489}
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