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Simplifying -20u2 + 4u + 11 = 0 Reorder the terms: 11 + 4u + -20u2 = 0 Solving 11 + 4u + -20u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -0.55 + -0.2u + u2 = 0 Move the constant term to the right: Add '0.55' to each side of the equation. -0.55 + -0.2u + 0.55 + u2 = 0 + 0.55 Reorder the terms: -0.55 + 0.55 + -0.2u + u2 = 0 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + -0.2u + u2 = 0 + 0.55 -0.2u + u2 = 0 + 0.55 Combine like terms: 0 + 0.55 = 0.55 -0.2u + u2 = 0.55 The u term is -0.2u. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2u + 0.01 + u2 = 0.55 + 0.01 Reorder the terms: 0.01 + -0.2u + u2 = 0.55 + 0.01 Combine like terms: 0.55 + 0.01 = 0.56 0.01 + -0.2u + u2 = 0.56 Factor a perfect square on the left side: (u + -0.1)(u + -0.1) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (u + -0.1) equal to 0.748331477 and -0.748331477.Subproblem 1
u + -0.1 = 0.748331477 Simplifying u + -0.1 = 0.748331477 Reorder the terms: -0.1 + u = 0.748331477 Solving -0.1 + u = 0.748331477 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + u = 0.748331477 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + u = 0.748331477 + 0.1 u = 0.748331477 + 0.1 Combine like terms: 0.748331477 + 0.1 = 0.848331477 u = 0.848331477 Simplifying u = 0.848331477Subproblem 2
u + -0.1 = -0.748331477 Simplifying u + -0.1 = -0.748331477 Reorder the terms: -0.1 + u = -0.748331477 Solving -0.1 + u = -0.748331477 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + u = -0.748331477 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + u = -0.748331477 + 0.1 u = -0.748331477 + 0.1 Combine like terms: -0.748331477 + 0.1 = -0.648331477 u = -0.648331477 Simplifying u = -0.648331477Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.848331477, -0.648331477}
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