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Simplifying -4u2 + 16u + -9 = 0 Reorder the terms: -9 + 16u + -4u2 = 0 Solving -9 + 16u + -4u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 2.25 + -4u + u2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -4u + -2.25 + u2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -4u + u2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -4u + u2 = 0 + -2.25 -4u + u2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -4u + u2 = -2.25 The u term is -4u. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4u + 4 + u2 = -2.25 + 4 Reorder the terms: 4 + -4u + u2 = -2.25 + 4 Combine like terms: -2.25 + 4 = 1.75 4 + -4u + u2 = 1.75 Factor a perfect square on the left side: (u + -2)(u + -2) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (u + -2) equal to 1.322875656 and -1.322875656.Subproblem 1
u + -2 = 1.322875656 Simplifying u + -2 = 1.322875656 Reorder the terms: -2 + u = 1.322875656 Solving -2 + u = 1.322875656 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + u = 1.322875656 + 2 Combine like terms: -2 + 2 = 0 0 + u = 1.322875656 + 2 u = 1.322875656 + 2 Combine like terms: 1.322875656 + 2 = 3.322875656 u = 3.322875656 Simplifying u = 3.322875656Subproblem 2
u + -2 = -1.322875656 Simplifying u + -2 = -1.322875656 Reorder the terms: -2 + u = -1.322875656 Solving -2 + u = -1.322875656 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + u = -1.322875656 + 2 Combine like terms: -2 + 2 = 0 0 + u = -1.322875656 + 2 u = -1.322875656 + 2 Combine like terms: -1.322875656 + 2 = 0.677124344 u = 0.677124344 Simplifying u = 0.677124344Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.322875656, 0.677124344}
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