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Simplifying 3u2 + -24u + 9 = 0 Reorder the terms: 9 + -24u + 3u2 = 0 Solving 9 + -24u + 3u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -8u + u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -8u + u2)' equal to zero and attempt to solve: Simplifying 3 + -8u + u2 = 0 Solving 3 + -8u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8u + -3 + u2 = 0 + -3 Reorder the terms: 3 + -3 + -8u + u2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8u + u2 = 0 + -3 -8u + u2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8u + u2 = -3 The u term is -8u. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8u + 16 + u2 = -3 + 16 Reorder the terms: 16 + -8u + u2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + -8u + u2 = 13 Factor a perfect square on the left side: (u + -4)(u + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (u + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
u + -4 = 3.605551275 Simplifying u + -4 = 3.605551275 Reorder the terms: -4 + u = 3.605551275 Solving -4 + u = 3.605551275 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + u = 3.605551275 + 4 u = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 u = 7.605551275 Simplifying u = 7.605551275Subproblem 2
u + -4 = -3.605551275 Simplifying u + -4 = -3.605551275 Reorder the terms: -4 + u = -3.605551275 Solving -4 + u = -3.605551275 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + u = -3.605551275 + 4 u = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 u = 0.394448725 Simplifying u = 0.394448725Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.605551275, 0.394448725}Solution
u = {7.605551275, 0.394448725}
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