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Simplifying 3u2 + -21u + -15 = 0 Reorder the terms: -15 + -21u + 3u2 = 0 Solving -15 + -21u + 3u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -7u + u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -7u + u2)' equal to zero and attempt to solve: Simplifying -5 + -7u + u2 = 0 Solving -5 + -7u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -7u + 5 + u2 = 0 + 5 Reorder the terms: -5 + 5 + -7u + u2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7u + u2 = 0 + 5 -7u + u2 = 0 + 5 Combine like terms: 0 + 5 = 5 -7u + u2 = 5 The u term is -7u. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7u + 12.25 + u2 = 5 + 12.25 Reorder the terms: 12.25 + -7u + u2 = 5 + 12.25 Combine like terms: 5 + 12.25 = 17.25 12.25 + -7u + u2 = 17.25 Factor a perfect square on the left side: (u + -3.5)(u + -3.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (u + -3.5) equal to 4.153311931 and -4.153311931.Subproblem 1
u + -3.5 = 4.153311931 Simplifying u + -3.5 = 4.153311931 Reorder the terms: -3.5 + u = 4.153311931 Solving -3.5 + u = 4.153311931 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + u = 4.153311931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + u = 4.153311931 + 3.5 u = 4.153311931 + 3.5 Combine like terms: 4.153311931 + 3.5 = 7.653311931 u = 7.653311931 Simplifying u = 7.653311931Subproblem 2
u + -3.5 = -4.153311931 Simplifying u + -3.5 = -4.153311931 Reorder the terms: -3.5 + u = -4.153311931 Solving -3.5 + u = -4.153311931 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + u = -4.153311931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + u = -4.153311931 + 3.5 u = -4.153311931 + 3.5 Combine like terms: -4.153311931 + 3.5 = -0.653311931 u = -0.653311931 Simplifying u = -0.653311931Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.653311931, -0.653311931}Solution
u = {7.653311931, -0.653311931}
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