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Simplifying 5u2 + 30u + -70 = 0 Reorder the terms: -70 + 30u + 5u2 = 0 Solving -70 + 30u + 5u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '5'. 5(-14 + 6u + u2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-14 + 6u + u2)' equal to zero and attempt to solve: Simplifying -14 + 6u + u2 = 0 Solving -14 + 6u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 6u + 14 + u2 = 0 + 14 Reorder the terms: -14 + 14 + 6u + u2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 6u + u2 = 0 + 14 6u + u2 = 0 + 14 Combine like terms: 0 + 14 = 14 6u + u2 = 14 The u term is 6u. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6u + 9 + u2 = 14 + 9 Reorder the terms: 9 + 6u + u2 = 14 + 9 Combine like terms: 14 + 9 = 23 9 + 6u + u2 = 23 Factor a perfect square on the left side: (u + 3)(u + 3) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (u + 3) equal to 4.795831523 and -4.795831523.Subproblem 1
u + 3 = 4.795831523 Simplifying u + 3 = 4.795831523 Reorder the terms: 3 + u = 4.795831523 Solving 3 + u = 4.795831523 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = 4.795831523 + -3 Combine like terms: 3 + -3 = 0 0 + u = 4.795831523 + -3 u = 4.795831523 + -3 Combine like terms: 4.795831523 + -3 = 1.795831523 u = 1.795831523 Simplifying u = 1.795831523Subproblem 2
u + 3 = -4.795831523 Simplifying u + 3 = -4.795831523 Reorder the terms: 3 + u = -4.795831523 Solving 3 + u = -4.795831523 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = -4.795831523 + -3 Combine like terms: 3 + -3 = 0 0 + u = -4.795831523 + -3 u = -4.795831523 + -3 Combine like terms: -4.795831523 + -3 = -7.795831523 u = -7.795831523 Simplifying u = -7.795831523Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.795831523, -7.795831523}Solution
u = {1.795831523, -7.795831523}
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