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Simplifying (-4u2 + 2u + 3) + (8u2 + -2u + -5) + -1(-1u2 + 9u + 8) = 0 Reorder the terms: (3 + 2u + -4u2) + (8u2 + -2u + -5) + -1(-1u2 + 9u + 8) = 0 Remove parenthesis around (3 + 2u + -4u2) 3 + 2u + -4u2 + (8u2 + -2u + -5) + -1(-1u2 + 9u + 8) = 0 Reorder the terms: 3 + 2u + -4u2 + (-5 + -2u + 8u2) + -1(-1u2 + 9u + 8) = 0 Remove parenthesis around (-5 + -2u + 8u2) 3 + 2u + -4u2 + -5 + -2u + 8u2 + -1(-1u2 + 9u + 8) = 0 Reorder the terms: 3 + 2u + -4u2 + -5 + -2u + 8u2 + -1(8 + 9u + -1u2) = 0 3 + 2u + -4u2 + -5 + -2u + 8u2 + (8 * -1 + 9u * -1 + -1u2 * -1) = 0 3 + 2u + -4u2 + -5 + -2u + 8u2 + (-8 + -9u + 1u2) = 0 Reorder the terms: 3 + -5 + -8 + 2u + -2u + -9u + -4u2 + 8u2 + 1u2 = 0 Combine like terms: 3 + -5 = -2 -2 + -8 + 2u + -2u + -9u + -4u2 + 8u2 + 1u2 = 0 Combine like terms: -2 + -8 = -10 -10 + 2u + -2u + -9u + -4u2 + 8u2 + 1u2 = 0 Combine like terms: 2u + -2u = 0 -10 + 0 + -9u + -4u2 + 8u2 + 1u2 = 0 -10 + -9u + -4u2 + 8u2 + 1u2 = 0 Combine like terms: -4u2 + 8u2 = 4u2 -10 + -9u + 4u2 + 1u2 = 0 Combine like terms: 4u2 + 1u2 = 5u2 -10 + -9u + 5u2 = 0 Solving -10 + -9u + 5u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -1.8u + u2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.8u + 2 + u2 = 0 + 2 Reorder the terms: -2 + 2 + -1.8u + u2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.8u + u2 = 0 + 2 -1.8u + u2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.8u + u2 = 2 The u term is -1.8u. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8u + 0.81 + u2 = 2 + 0.81 Reorder the terms: 0.81 + -1.8u + u2 = 2 + 0.81 Combine like terms: 2 + 0.81 = 2.81 0.81 + -1.8u + u2 = 2.81 Factor a perfect square on the left side: (u + -0.9)(u + -0.9) = 2.81 Calculate the square root of the right side: 1.676305461 Break this problem into two subproblems by setting (u + -0.9) equal to 1.676305461 and -1.676305461.Subproblem 1
u + -0.9 = 1.676305461 Simplifying u + -0.9 = 1.676305461 Reorder the terms: -0.9 + u = 1.676305461 Solving -0.9 + u = 1.676305461 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + u = 1.676305461 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + u = 1.676305461 + 0.9 u = 1.676305461 + 0.9 Combine like terms: 1.676305461 + 0.9 = 2.576305461 u = 2.576305461 Simplifying u = 2.576305461Subproblem 2
u + -0.9 = -1.676305461 Simplifying u + -0.9 = -1.676305461 Reorder the terms: -0.9 + u = -1.676305461 Solving -0.9 + u = -1.676305461 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + u = -1.676305461 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + u = -1.676305461 + 0.9 u = -1.676305461 + 0.9 Combine like terms: -1.676305461 + 0.9 = -0.776305461 u = -0.776305461 Simplifying u = -0.776305461Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.576305461, -0.776305461}
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