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Simplifying 3u(3u) = -4u + 15 Remove parenthesis around (3u) 3u * 3u = -4u + 15 Reorder the terms for easier multiplication: 3 * 3u * u = -4u + 15 Multiply 3 * 3 9u * u = -4u + 15 Multiply u * u 9u2 = -4u + 15 Reorder the terms: 9u2 = 15 + -4u Solving 9u2 = 15 + -4u Solving for variable 'u'. Reorder the terms: -15 + 4u + 9u2 = 15 + -4u + -15 + 4u Reorder the terms: -15 + 4u + 9u2 = 15 + -15 + -4u + 4u Combine like terms: 15 + -15 = 0 -15 + 4u + 9u2 = 0 + -4u + 4u -15 + 4u + 9u2 = -4u + 4u Combine like terms: -4u + 4u = 0 -15 + 4u + 9u2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.666666667 + 0.4444444444u + u2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 0.4444444444u + 1.666666667 + u2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 0.4444444444u + u2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 0.4444444444u + u2 = 0 + 1.666666667 0.4444444444u + u2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 0.4444444444u + u2 = 1.666666667 The u term is 0.4444444444u. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444u + 0.04938271604 + u2 = 1.666666667 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444u + u2 = 1.666666667 + 0.04938271604 Combine like terms: 1.666666667 + 0.04938271604 = 1.71604938304 0.04938271604 + 0.4444444444u + u2 = 1.71604938304 Factor a perfect square on the left side: (u + 0.2222222222)(u + 0.2222222222) = 1.71604938304 Calculate the square root of the right side: 1.30998068 Break this problem into two subproblems by setting (u + 0.2222222222) equal to 1.30998068 and -1.30998068.Subproblem 1
u + 0.2222222222 = 1.30998068 Simplifying u + 0.2222222222 = 1.30998068 Reorder the terms: 0.2222222222 + u = 1.30998068 Solving 0.2222222222 + u = 1.30998068 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + u = 1.30998068 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + u = 1.30998068 + -0.2222222222 u = 1.30998068 + -0.2222222222 Combine like terms: 1.30998068 + -0.2222222222 = 1.0877584578 u = 1.0877584578 Simplifying u = 1.0877584578Subproblem 2
u + 0.2222222222 = -1.30998068 Simplifying u + 0.2222222222 = -1.30998068 Reorder the terms: 0.2222222222 + u = -1.30998068 Solving 0.2222222222 + u = -1.30998068 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + u = -1.30998068 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + u = -1.30998068 + -0.2222222222 u = -1.30998068 + -0.2222222222 Combine like terms: -1.30998068 + -0.2222222222 = -1.5322029022 u = -1.5322029022 Simplifying u = -1.5322029022Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.0877584578, -1.5322029022}
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