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Simplifying -4u2 + 52u + -132 = 0 Reorder the terms: -132 + 52u + -4u2 = 0 Solving -132 + 52u + -4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '4'. 4(-33 + 13u + -1u2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-33 + 13u + -1u2)' equal to zero and attempt to solve: Simplifying -33 + 13u + -1u2 = 0 Solving -33 + 13u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 33 + -13u + u2 = 0 Move the constant term to the right: Add '-33' to each side of the equation. 33 + -13u + -33 + u2 = 0 + -33 Reorder the terms: 33 + -33 + -13u + u2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -13u + u2 = 0 + -33 -13u + u2 = 0 + -33 Combine like terms: 0 + -33 = -33 -13u + u2 = -33 The u term is -13u. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13u + 42.25 + u2 = -33 + 42.25 Reorder the terms: 42.25 + -13u + u2 = -33 + 42.25 Combine like terms: -33 + 42.25 = 9.25 42.25 + -13u + u2 = 9.25 Factor a perfect square on the left side: (u + -6.5)(u + -6.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (u + -6.5) equal to 3.041381265 and -3.041381265.Subproblem 1
u + -6.5 = 3.041381265 Simplifying u + -6.5 = 3.041381265 Reorder the terms: -6.5 + u = 3.041381265 Solving -6.5 + u = 3.041381265 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + u = 3.041381265 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + u = 3.041381265 + 6.5 u = 3.041381265 + 6.5 Combine like terms: 3.041381265 + 6.5 = 9.541381265 u = 9.541381265 Simplifying u = 9.541381265Subproblem 2
u + -6.5 = -3.041381265 Simplifying u + -6.5 = -3.041381265 Reorder the terms: -6.5 + u = -3.041381265 Solving -6.5 + u = -3.041381265 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + u = -3.041381265 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + u = -3.041381265 + 6.5 u = -3.041381265 + 6.5 Combine like terms: -3.041381265 + 6.5 = 3.458618735 u = 3.458618735 Simplifying u = 3.458618735Solution
The solution to the problem is based on the solutions from the subproblems. u = {9.541381265, 3.458618735}Solution
u = {9.541381265, 3.458618735}
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