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Simplifying -2u2 + 15u + 25 = 0 Reorder the terms: 25 + 15u + -2u2 = 0 Solving 25 + 15u + -2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.5 + -7.5u + u2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -7.5u + 12.5 + u2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -7.5u + u2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -7.5u + u2 = 0 + 12.5 -7.5u + u2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -7.5u + u2 = 12.5 The u term is -7.5u. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5u + 14.0625 + u2 = 12.5 + 14.0625 Reorder the terms: 14.0625 + -7.5u + u2 = 12.5 + 14.0625 Combine like terms: 12.5 + 14.0625 = 26.5625 14.0625 + -7.5u + u2 = 26.5625 Factor a perfect square on the left side: (u + -3.75)(u + -3.75) = 26.5625 Calculate the square root of the right side: 5.153882032 Break this problem into two subproblems by setting (u + -3.75) equal to 5.153882032 and -5.153882032.Subproblem 1
u + -3.75 = 5.153882032 Simplifying u + -3.75 = 5.153882032 Reorder the terms: -3.75 + u = 5.153882032 Solving -3.75 + u = 5.153882032 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + u = 5.153882032 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + u = 5.153882032 + 3.75 u = 5.153882032 + 3.75 Combine like terms: 5.153882032 + 3.75 = 8.903882032 u = 8.903882032 Simplifying u = 8.903882032Subproblem 2
u + -3.75 = -5.153882032 Simplifying u + -3.75 = -5.153882032 Reorder the terms: -3.75 + u = -5.153882032 Solving -3.75 + u = -5.153882032 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + u = -5.153882032 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + u = -5.153882032 + 3.75 u = -5.153882032 + 3.75 Combine like terms: -5.153882032 + 3.75 = -1.403882032 u = -1.403882032 Simplifying u = -1.403882032Solution
The solution to the problem is based on the solutions from the subproblems. u = {8.903882032, -1.403882032}
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