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Simplifying 5u2 + 15u + -28 = 0 Reorder the terms: -28 + 15u + 5u2 = 0 Solving -28 + 15u + 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'. -5.6 + 3u + u2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 3u + 5.6 + u2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 3u + u2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 3u + u2 = 0 + 5.6 3u + u2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 3u + u2 = 5.6 The u term is 3u. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3u + 2.25 + u2 = 5.6 + 2.25 Reorder the terms: 2.25 + 3u + u2 = 5.6 + 2.25 Combine like terms: 5.6 + 2.25 = 7.85 2.25 + 3u + u2 = 7.85 Factor a perfect square on the left side: (u + 1.5)(u + 1.5) = 7.85 Calculate the square root of the right side: 2.801785145 Break this problem into two subproblems by setting (u + 1.5) equal to 2.801785145 and -2.801785145.Subproblem 1
u + 1.5 = 2.801785145 Simplifying u + 1.5 = 2.801785145 Reorder the terms: 1.5 + u = 2.801785145 Solving 1.5 + u = 2.801785145 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + u = 2.801785145 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + u = 2.801785145 + -1.5 u = 2.801785145 + -1.5 Combine like terms: 2.801785145 + -1.5 = 1.301785145 u = 1.301785145 Simplifying u = 1.301785145Subproblem 2
u + 1.5 = -2.801785145 Simplifying u + 1.5 = -2.801785145 Reorder the terms: 1.5 + u = -2.801785145 Solving 1.5 + u = -2.801785145 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + u = -2.801785145 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + u = -2.801785145 + -1.5 u = -2.801785145 + -1.5 Combine like terms: -2.801785145 + -1.5 = -4.301785145 u = -4.301785145 Simplifying u = -4.301785145Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.301785145, -4.301785145}
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