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Simplifying 2u2 + -7u + -6 = 0 Reorder the terms: -6 + -7u + 2u2 = 0 Solving -6 + -7u + 2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + -3.5u + u2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3.5u + 3 + u2 = 0 + 3 Reorder the terms: -3 + 3 + -3.5u + u2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3.5u + u2 = 0 + 3 -3.5u + u2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3.5u + u2 = 3 The u term is -3.5u. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5u + 3.0625 + u2 = 3 + 3.0625 Reorder the terms: 3.0625 + -3.5u + u2 = 3 + 3.0625 Combine like terms: 3 + 3.0625 = 6.0625 3.0625 + -3.5u + u2 = 6.0625 Factor a perfect square on the left side: (u + -1.75)(u + -1.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (u + -1.75) equal to 2.46221445 and -2.46221445.Subproblem 1
u + -1.75 = 2.46221445 Simplifying u + -1.75 = 2.46221445 Reorder the terms: -1.75 + u = 2.46221445 Solving -1.75 + u = 2.46221445 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + u = 2.46221445 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + u = 2.46221445 + 1.75 u = 2.46221445 + 1.75 Combine like terms: 2.46221445 + 1.75 = 4.21221445 u = 4.21221445 Simplifying u = 4.21221445Subproblem 2
u + -1.75 = -2.46221445 Simplifying u + -1.75 = -2.46221445 Reorder the terms: -1.75 + u = -2.46221445 Solving -1.75 + u = -2.46221445 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + u = -2.46221445 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + u = -2.46221445 + 1.75 u = -2.46221445 + 1.75 Combine like terms: -2.46221445 + 1.75 = -0.71221445 u = -0.71221445 Simplifying u = -0.71221445Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.21221445, -0.71221445}
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