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Simplifying -13u2 + u + 36 = 0 Reorder the terms: 36 + u + -13u2 = 0 Solving 36 + u + -13u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -2.769230769 + -0.07692307692u + u2 = 0 Move the constant term to the right: Add '2.769230769' to each side of the equation. -2.769230769 + -0.07692307692u + 2.769230769 + u2 = 0 + 2.769230769 Reorder the terms: -2.769230769 + 2.769230769 + -0.07692307692u + u2 = 0 + 2.769230769 Combine like terms: -2.769230769 + 2.769230769 = 0.000000000 0.000000000 + -0.07692307692u + u2 = 0 + 2.769230769 -0.07692307692u + u2 = 0 + 2.769230769 Combine like terms: 0 + 2.769230769 = 2.769230769 -0.07692307692u + u2 = 2.769230769 The u term is u. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.07692307692u + 0.25 + u2 = 2.769230769 + 0.25 Reorder the terms: 0.25 + -0.07692307692u + u2 = 2.769230769 + 0.25 Combine like terms: 2.769230769 + 0.25 = 3.019230769 0.25 + -0.07692307692u + u2 = 3.019230769 Factor a perfect square on the left side: (u + 0.5)(u + 0.5) = 3.019230769 Calculate the square root of the right side: 1.737593384 Break this problem into two subproblems by setting (u + 0.5) equal to 1.737593384 and -1.737593384.Subproblem 1
u + 0.5 = 1.737593384 Simplifying u + 0.5 = 1.737593384 Reorder the terms: 0.5 + u = 1.737593384 Solving 0.5 + u = 1.737593384 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + u = 1.737593384 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = 1.737593384 + -0.5 u = 1.737593384 + -0.5 Combine like terms: 1.737593384 + -0.5 = 1.237593384 u = 1.237593384 Simplifying u = 1.237593384Subproblem 2
u + 0.5 = -1.737593384 Simplifying u + 0.5 = -1.737593384 Reorder the terms: 0.5 + u = -1.737593384 Solving 0.5 + u = -1.737593384 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + u = -1.737593384 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = -1.737593384 + -0.5 u = -1.737593384 + -0.5 Combine like terms: -1.737593384 + -0.5 = -2.237593384 u = -2.237593384 Simplifying u = -2.237593384Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.237593384, -2.237593384}
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