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Simplifying 7u2 + -3u + -7 = 0 Reorder the terms: -7 + -3u + 7u2 = 0 Solving -7 + -3u + 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'. -1 + -0.4285714286u + u2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.4285714286u + 1 + u2 = 0 + 1 Reorder the terms: -1 + 1 + -0.4285714286u + u2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.4285714286u + u2 = 0 + 1 -0.4285714286u + u2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.4285714286u + u2 = 1 The u term is -0.4285714286u. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286u + 0.04591836735 + u2 = 1 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286u + u2 = 1 + 0.04591836735 Combine like terms: 1 + 0.04591836735 = 1.04591836735 0.04591836735 + -0.4285714286u + u2 = 1.04591836735 Factor a perfect square on the left side: (u + -0.2142857143)(u + -0.2142857143) = 1.04591836735 Calculate the square root of the right side: 1.022701505 Break this problem into two subproblems by setting (u + -0.2142857143) equal to 1.022701505 and -1.022701505.Subproblem 1
u + -0.2142857143 = 1.022701505 Simplifying u + -0.2142857143 = 1.022701505 Reorder the terms: -0.2142857143 + u = 1.022701505 Solving -0.2142857143 + u = 1.022701505 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + u = 1.022701505 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + u = 1.022701505 + 0.2142857143 u = 1.022701505 + 0.2142857143 Combine like terms: 1.022701505 + 0.2142857143 = 1.2369872193 u = 1.2369872193 Simplifying u = 1.2369872193Subproblem 2
u + -0.2142857143 = -1.022701505 Simplifying u + -0.2142857143 = -1.022701505 Reorder the terms: -0.2142857143 + u = -1.022701505 Solving -0.2142857143 + u = -1.022701505 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + u = -1.022701505 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + u = -1.022701505 + 0.2142857143 u = -1.022701505 + 0.2142857143 Combine like terms: -1.022701505 + 0.2142857143 = -0.8084157907 u = -0.8084157907 Simplifying u = -0.8084157907Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.2369872193, -0.8084157907}
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