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Simplifying 10u2 + -9 + u + 2 = 0 Reorder the terms: -9 + 2 + u + 10u2 = 0 Combine like terms: -9 + 2 = -7 -7 + u + 10u2 = 0 Solving -7 + u + 10u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + 0.1u + u2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + 0.1u + 0.7 + u2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + 0.1u + u2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + 0.1u + u2 = 0 + 0.7 0.1u + u2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 0.1u + u2 = 0.7 The u term is u. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1u + 0.25 + u2 = 0.7 + 0.25 Reorder the terms: 0.25 + 0.1u + u2 = 0.7 + 0.25 Combine like terms: 0.7 + 0.25 = 0.95 0.25 + 0.1u + u2 = 0.95 Factor a perfect square on the left side: (u + 0.5)(u + 0.5) = 0.95 Calculate the square root of the right side: 0.974679434 Break this problem into two subproblems by setting (u + 0.5) equal to 0.974679434 and -0.974679434.Subproblem 1
u + 0.5 = 0.974679434 Simplifying u + 0.5 = 0.974679434 Reorder the terms: 0.5 + u = 0.974679434 Solving 0.5 + u = 0.974679434 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + u = 0.974679434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = 0.974679434 + -0.5 u = 0.974679434 + -0.5 Combine like terms: 0.974679434 + -0.5 = 0.474679434 u = 0.474679434 Simplifying u = 0.474679434Subproblem 2
u + 0.5 = -0.974679434 Simplifying u + 0.5 = -0.974679434 Reorder the terms: 0.5 + u = -0.974679434 Solving 0.5 + u = -0.974679434 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + u = -0.974679434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = -0.974679434 + -0.5 u = -0.974679434 + -0.5 Combine like terms: -0.974679434 + -0.5 = -1.474679434 u = -1.474679434 Simplifying u = -1.474679434Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.474679434, -1.474679434}
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