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Simplifying -4u2 = -8u + -3 Reorder the terms: -4u2 = -3 + -8u Solving -4u2 = -3 + -8u Solving for variable 'u'. Reorder the terms: 3 + 8u + -4u2 = -3 + -8u + 3 + 8u Reorder the terms: 3 + 8u + -4u2 = -3 + 3 + -8u + 8u Combine like terms: -3 + 3 = 0 3 + 8u + -4u2 = 0 + -8u + 8u 3 + 8u + -4u2 = -8u + 8u Combine like terms: -8u + 8u = 0 3 + 8u + -4u2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -2u + u2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2u + 0.75 + u2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2u + u2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2u + u2 = 0 + 0.75 -2u + u2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2u + u2 = 0.75 The u term is -2u. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2u + 1 + u2 = 0.75 + 1 Reorder the terms: 1 + -2u + u2 = 0.75 + 1 Combine like terms: 0.75 + 1 = 1.75 1 + -2u + u2 = 1.75 Factor a perfect square on the left side: (u + -1)(u + -1) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (u + -1) equal to 1.322875656 and -1.322875656.Subproblem 1
u + -1 = 1.322875656 Simplifying u + -1 = 1.322875656 Reorder the terms: -1 + u = 1.322875656 Solving -1 + u = 1.322875656 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u = 1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + u = 1.322875656 + 1 u = 1.322875656 + 1 Combine like terms: 1.322875656 + 1 = 2.322875656 u = 2.322875656 Simplifying u = 2.322875656Subproblem 2
u + -1 = -1.322875656 Simplifying u + -1 = -1.322875656 Reorder the terms: -1 + u = -1.322875656 Solving -1 + u = -1.322875656 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u = -1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + u = -1.322875656 + 1 u = -1.322875656 + 1 Combine like terms: -1.322875656 + 1 = -0.322875656 u = -0.322875656 Simplifying u = -0.322875656Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.322875656, -0.322875656}
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