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Simplifying u2 = 12u + -3 Reorder the terms: u2 = -3 + 12u Solving u2 = -3 + 12u Solving for variable 'u'. Reorder the terms: 3 + -12u + u2 = -3 + 12u + 3 + -12u Reorder the terms: 3 + -12u + u2 = -3 + 3 + 12u + -12u Combine like terms: -3 + 3 = 0 3 + -12u + u2 = 0 + 12u + -12u 3 + -12u + u2 = 12u + -12u Combine like terms: 12u + -12u = 0 3 + -12u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -12u + -3 + u2 = 0 + -3 Reorder the terms: 3 + -3 + -12u + u2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -12u + u2 = 0 + -3 -12u + u2 = 0 + -3 Combine like terms: 0 + -3 = -3 -12u + u2 = -3 The u term is -12u. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12u + 36 + u2 = -3 + 36 Reorder the terms: 36 + -12u + u2 = -3 + 36 Combine like terms: -3 + 36 = 33 36 + -12u + u2 = 33 Factor a perfect square on the left side: (u + -6)(u + -6) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (u + -6) equal to 5.744562647 and -5.744562647.Subproblem 1
u + -6 = 5.744562647 Simplifying u + -6 = 5.744562647 Reorder the terms: -6 + u = 5.744562647 Solving -6 + u = 5.744562647 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + u = 5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + u = 5.744562647 + 6 u = 5.744562647 + 6 Combine like terms: 5.744562647 + 6 = 11.744562647 u = 11.744562647 Simplifying u = 11.744562647Subproblem 2
u + -6 = -5.744562647 Simplifying u + -6 = -5.744562647 Reorder the terms: -6 + u = -5.744562647 Solving -6 + u = -5.744562647 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + u = -5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + u = -5.744562647 + 6 u = -5.744562647 + 6 Combine like terms: -5.744562647 + 6 = 0.255437353 u = 0.255437353 Simplifying u = 0.255437353Solution
The solution to the problem is based on the solutions from the subproblems. u = {11.744562647, 0.255437353}
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