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Simplifying u2 + 24u = 19 Reorder the terms: 24u + u2 = 19 Solving 24u + u2 = 19 Solving for variable 'u'. Reorder the terms: -19 + 24u + u2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 24u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 24u + 19 + u2 = 0 + 19 Reorder the terms: -19 + 19 + 24u + u2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 24u + u2 = 0 + 19 24u + u2 = 0 + 19 Combine like terms: 0 + 19 = 19 24u + u2 = 19 The u term is 24u. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24u + 144 + u2 = 19 + 144 Reorder the terms: 144 + 24u + u2 = 19 + 144 Combine like terms: 19 + 144 = 163 144 + 24u + u2 = 163 Factor a perfect square on the left side: (u + 12)(u + 12) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (u + 12) equal to 12.767145335 and -12.767145335.Subproblem 1
u + 12 = 12.767145335 Simplifying u + 12 = 12.767145335 Reorder the terms: 12 + u = 12.767145335 Solving 12 + u = 12.767145335 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + u = 12.767145335 + -12 Combine like terms: 12 + -12 = 0 0 + u = 12.767145335 + -12 u = 12.767145335 + -12 Combine like terms: 12.767145335 + -12 = 0.767145335 u = 0.767145335 Simplifying u = 0.767145335Subproblem 2
u + 12 = -12.767145335 Simplifying u + 12 = -12.767145335 Reorder the terms: 12 + u = -12.767145335 Solving 12 + u = -12.767145335 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + u = -12.767145335 + -12 Combine like terms: 12 + -12 = 0 0 + u = -12.767145335 + -12 u = -12.767145335 + -12 Combine like terms: -12.767145335 + -12 = -24.767145335 u = -24.767145335 Simplifying u = -24.767145335Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.767145335, -24.767145335}
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