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Simplifying -7u(u + -7) = -4 Reorder the terms: -7u(-7 + u) = -4 (-7 * -7u + u * -7u) = -4 (49u + -7u2) = -4 Solving 49u + -7u2 = -4 Solving for variable 'u'. Reorder the terms: 4 + 49u + -7u2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 49u + -7u2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.5714285714 + -7u + u2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -7u + 0.5714285714 + u2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -7u + u2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -7u + u2 = 0 + 0.5714285714 -7u + u2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -7u + u2 = 0.5714285714 The u term is -7u. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7u + 12.25 + u2 = 0.5714285714 + 12.25 Reorder the terms: 12.25 + -7u + u2 = 0.5714285714 + 12.25 Combine like terms: 0.5714285714 + 12.25 = 12.8214285714 12.25 + -7u + u2 = 12.8214285714 Factor a perfect square on the left side: (u + -3.5)(u + -3.5) = 12.8214285714 Calculate the square root of the right side: 3.580702246 Break this problem into two subproblems by setting (u + -3.5) equal to 3.580702246 and -3.580702246.Subproblem 1
u + -3.5 = 3.580702246 Simplifying u + -3.5 = 3.580702246 Reorder the terms: -3.5 + u = 3.580702246 Solving -3.5 + u = 3.580702246 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + u = 3.580702246 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + u = 3.580702246 + 3.5 u = 3.580702246 + 3.5 Combine like terms: 3.580702246 + 3.5 = 7.080702246 u = 7.080702246 Simplifying u = 7.080702246Subproblem 2
u + -3.5 = -3.580702246 Simplifying u + -3.5 = -3.580702246 Reorder the terms: -3.5 + u = -3.580702246 Solving -3.5 + u = -3.580702246 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + u = -3.580702246 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + u = -3.580702246 + 3.5 u = -3.580702246 + 3.5 Combine like terms: -3.580702246 + 3.5 = -0.080702246 u = -0.080702246 Simplifying u = -0.080702246Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.080702246, -0.080702246}
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