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Simplifying 7u2 + 2u + -4 = 0 Reorder the terms: -4 + 2u + 7u2 = 0 Solving -4 + 2u + 7u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + 0.2857142857u + u2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 0.2857142857u + 0.5714285714 + u2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 0.2857142857u + u2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 0.2857142857u + u2 = 0 + 0.5714285714 0.2857142857u + u2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 0.2857142857u + u2 = 0.5714285714 The u term is 0.2857142857u. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857u + 0.02040816328 + u2 = 0.5714285714 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857u + u2 = 0.5714285714 + 0.02040816328 Combine like terms: 0.5714285714 + 0.02040816328 = 0.59183673468 0.02040816328 + 0.2857142857u + u2 = 0.59183673468 Factor a perfect square on the left side: (u + 0.1428571429)(u + 0.1428571429) = 0.59183673468 Calculate the square root of the right side: 0.769309258 Break this problem into two subproblems by setting (u + 0.1428571429) equal to 0.769309258 and -0.769309258.Subproblem 1
u + 0.1428571429 = 0.769309258 Simplifying u + 0.1428571429 = 0.769309258 Reorder the terms: 0.1428571429 + u = 0.769309258 Solving 0.1428571429 + u = 0.769309258 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + u = 0.769309258 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + u = 0.769309258 + -0.1428571429 u = 0.769309258 + -0.1428571429 Combine like terms: 0.769309258 + -0.1428571429 = 0.6264521151 u = 0.6264521151 Simplifying u = 0.6264521151Subproblem 2
u + 0.1428571429 = -0.769309258 Simplifying u + 0.1428571429 = -0.769309258 Reorder the terms: 0.1428571429 + u = -0.769309258 Solving 0.1428571429 + u = -0.769309258 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + u = -0.769309258 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + u = -0.769309258 + -0.1428571429 u = -0.769309258 + -0.1428571429 Combine like terms: -0.769309258 + -0.1428571429 = -0.9121664009 u = -0.9121664009 Simplifying u = -0.9121664009Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.6264521151, -0.9121664009}
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