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Simplifying 5u2 + 8u + -10 = 0 Reorder the terms: -10 + 8u + 5u2 = 0 Solving -10 + 8u + 5u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + 1.6u + u2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.6u + 2 + u2 = 0 + 2 Reorder the terms: -2 + 2 + 1.6u + u2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.6u + u2 = 0 + 2 1.6u + u2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.6u + u2 = 2 The u term is 1.6u. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6u + 0.64 + u2 = 2 + 0.64 Reorder the terms: 0.64 + 1.6u + u2 = 2 + 0.64 Combine like terms: 2 + 0.64 = 2.64 0.64 + 1.6u + u2 = 2.64 Factor a perfect square on the left side: (u + 0.8)(u + 0.8) = 2.64 Calculate the square root of the right side: 1.624807681 Break this problem into two subproblems by setting (u + 0.8) equal to 1.624807681 and -1.624807681.Subproblem 1
u + 0.8 = 1.624807681 Simplifying u + 0.8 = 1.624807681 Reorder the terms: 0.8 + u = 1.624807681 Solving 0.8 + u = 1.624807681 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + u = 1.624807681 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + u = 1.624807681 + -0.8 u = 1.624807681 + -0.8 Combine like terms: 1.624807681 + -0.8 = 0.824807681 u = 0.824807681 Simplifying u = 0.824807681Subproblem 2
u + 0.8 = -1.624807681 Simplifying u + 0.8 = -1.624807681 Reorder the terms: 0.8 + u = -1.624807681 Solving 0.8 + u = -1.624807681 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + u = -1.624807681 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + u = -1.624807681 + -0.8 u = -1.624807681 + -0.8 Combine like terms: -1.624807681 + -0.8 = -2.424807681 u = -2.424807681 Simplifying u = -2.424807681Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.824807681, -2.424807681}
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