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Simplifying 5u2 + 3u + -70 = 0 Reorder the terms: -70 + 3u + 5u2 = 0 Solving -70 + 3u + 5u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14 + 0.6u + u2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 0.6u + 14 + u2 = 0 + 14 Reorder the terms: -14 + 14 + 0.6u + u2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 0.6u + u2 = 0 + 14 0.6u + u2 = 0 + 14 Combine like terms: 0 + 14 = 14 0.6u + u2 = 14 The u term is 0.6u. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6u + 0.09 + u2 = 14 + 0.09 Reorder the terms: 0.09 + 0.6u + u2 = 14 + 0.09 Combine like terms: 14 + 0.09 = 14.09 0.09 + 0.6u + u2 = 14.09 Factor a perfect square on the left side: (u + 0.3)(u + 0.3) = 14.09 Calculate the square root of the right side: 3.753664876 Break this problem into two subproblems by setting (u + 0.3) equal to 3.753664876 and -3.753664876.Subproblem 1
u + 0.3 = 3.753664876 Simplifying u + 0.3 = 3.753664876 Reorder the terms: 0.3 + u = 3.753664876 Solving 0.3 + u = 3.753664876 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + u = 3.753664876 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + u = 3.753664876 + -0.3 u = 3.753664876 + -0.3 Combine like terms: 3.753664876 + -0.3 = 3.453664876 u = 3.453664876 Simplifying u = 3.453664876Subproblem 2
u + 0.3 = -3.753664876 Simplifying u + 0.3 = -3.753664876 Reorder the terms: 0.3 + u = -3.753664876 Solving 0.3 + u = -3.753664876 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + u = -3.753664876 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + u = -3.753664876 + -0.3 u = -3.753664876 + -0.3 Combine like terms: -3.753664876 + -0.3 = -4.053664876 u = -4.053664876 Simplifying u = -4.053664876Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.453664876, -4.053664876}
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