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Simplifying (5u2 + -1u + -7) = 0 Reorder the terms: (-7 + -1u + 5u2) = 0 Remove parenthesis around (-7 + -1u + 5u2) -7 + -1u + 5u2 = 0 Solving -7 + -1u + 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'. -1.4 + -0.2u + u2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.2u + 1.4 + u2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.2u + u2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.2u + u2 = 0 + 1.4 -0.2u + u2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.2u + u2 = 1.4 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 = 1.4 + 0.01 Reorder the terms: 0.01 + -0.2u + u2 = 1.4 + 0.01 Combine like terms: 1.4 + 0.01 = 1.41 0.01 + -0.2u + u2 = 1.41 Factor a perfect square on the left side: (u + -0.1)(u + -0.1) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (u + -0.1) equal to 1.187434209 and -1.187434209.Subproblem 1
u + -0.1 = 1.187434209 Simplifying u + -0.1 = 1.187434209 Reorder the terms: -0.1 + u = 1.187434209 Solving -0.1 + u = 1.187434209 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 = 1.187434209 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + u = 1.187434209 + 0.1 u = 1.187434209 + 0.1 Combine like terms: 1.187434209 + 0.1 = 1.287434209 u = 1.287434209 Simplifying u = 1.287434209Subproblem 2
u + -0.1 = -1.187434209 Simplifying u + -0.1 = -1.187434209 Reorder the terms: -0.1 + u = -1.187434209 Solving -0.1 + u = -1.187434209 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 = -1.187434209 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + u = -1.187434209 + 0.1 u = -1.187434209 + 0.1 Combine like terms: -1.187434209 + 0.1 = -1.087434209 u = -1.087434209 Simplifying u = -1.087434209Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.287434209, -1.087434209}
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