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Simplifying (-7u2 + 8u + 7) + -1(2u2 + -9u + -5) + (-7u2 + 5u + -7) = 0 Reorder the terms: (7 + 8u + -7u2) + -1(2u2 + -9u + -5) + (-7u2 + 5u + -7) = 0 Remove parenthesis around (7 + 8u + -7u2) 7 + 8u + -7u2 + -1(2u2 + -9u + -5) + (-7u2 + 5u + -7) = 0 Reorder the terms: 7 + 8u + -7u2 + -1(-5 + -9u + 2u2) + (-7u2 + 5u + -7) = 0 7 + 8u + -7u2 + (-5 * -1 + -9u * -1 + 2u2 * -1) + (-7u2 + 5u + -7) = 0 7 + 8u + -7u2 + (5 + 9u + -2u2) + (-7u2 + 5u + -7) = 0 Reorder the terms: 7 + 8u + -7u2 + 5 + 9u + -2u2 + (-7 + 5u + -7u2) = 0 Remove parenthesis around (-7 + 5u + -7u2) 7 + 8u + -7u2 + 5 + 9u + -2u2 + -7 + 5u + -7u2 = 0 Reorder the terms: 7 + 5 + -7 + 8u + 9u + 5u + -7u2 + -2u2 + -7u2 = 0 Combine like terms: 7 + 5 = 12 12 + -7 + 8u + 9u + 5u + -7u2 + -2u2 + -7u2 = 0 Combine like terms: 12 + -7 = 5 5 + 8u + 9u + 5u + -7u2 + -2u2 + -7u2 = 0 Combine like terms: 8u + 9u = 17u 5 + 17u + 5u + -7u2 + -2u2 + -7u2 = 0 Combine like terms: 17u + 5u = 22u 5 + 22u + -7u2 + -2u2 + -7u2 = 0 Combine like terms: -7u2 + -2u2 = -9u2 5 + 22u + -9u2 + -7u2 = 0 Combine like terms: -9u2 + -7u2 = -16u2 5 + 22u + -16u2 = 0 Solving 5 + 22u + -16u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + -1.375u + u2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -1.375u + 0.3125 + u2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -1.375u + u2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -1.375u + u2 = 0 + 0.3125 -1.375u + u2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -1.375u + u2 = 0.3125 The u term is -1.375u. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375u + 0.47265625 + u2 = 0.3125 + 0.47265625 Reorder the terms: 0.47265625 + -1.375u + u2 = 0.3125 + 0.47265625 Combine like terms: 0.3125 + 0.47265625 = 0.78515625 0.47265625 + -1.375u + u2 = 0.78515625 Factor a perfect square on the left side: (u + -0.6875)(u + -0.6875) = 0.78515625 Calculate the square root of the right side: 0.88609043 Break this problem into two subproblems by setting (u + -0.6875) equal to 0.88609043 and -0.88609043.Subproblem 1
u + -0.6875 = 0.88609043 Simplifying u + -0.6875 = 0.88609043 Reorder the terms: -0.6875 + u = 0.88609043 Solving -0.6875 + u = 0.88609043 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + u = 0.88609043 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + u = 0.88609043 + 0.6875 u = 0.88609043 + 0.6875 Combine like terms: 0.88609043 + 0.6875 = 1.57359043 u = 1.57359043 Simplifying u = 1.57359043Subproblem 2
u + -0.6875 = -0.88609043 Simplifying u + -0.6875 = -0.88609043 Reorder the terms: -0.6875 + u = -0.88609043 Solving -0.6875 + u = -0.88609043 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + u = -0.88609043 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + u = -0.88609043 + 0.6875 u = -0.88609043 + 0.6875 Combine like terms: -0.88609043 + 0.6875 = -0.19859043 u = -0.19859043 Simplifying u = -0.19859043Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.57359043, -0.19859043}
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