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Simplifying 5u2 + -32u + -35 = 0 Reorder the terms: -35 + -32u + 5u2 = 0 Solving -35 + -32u + 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'. -7 + -6.4u + u2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -6.4u + 7 + u2 = 0 + 7 Reorder the terms: -7 + 7 + -6.4u + u2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6.4u + u2 = 0 + 7 -6.4u + u2 = 0 + 7 Combine like terms: 0 + 7 = 7 -6.4u + u2 = 7 The u term is -6.4u. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4u + 10.24 + u2 = 7 + 10.24 Reorder the terms: 10.24 + -6.4u + u2 = 7 + 10.24 Combine like terms: 7 + 10.24 = 17.24 10.24 + -6.4u + u2 = 17.24 Factor a perfect square on the left side: (u + -3.2)(u + -3.2) = 17.24 Calculate the square root of the right side: 4.152107898 Break this problem into two subproblems by setting (u + -3.2) equal to 4.152107898 and -4.152107898.Subproblem 1
u + -3.2 = 4.152107898 Simplifying u + -3.2 = 4.152107898 Reorder the terms: -3.2 + u = 4.152107898 Solving -3.2 + u = 4.152107898 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + u = 4.152107898 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + u = 4.152107898 + 3.2 u = 4.152107898 + 3.2 Combine like terms: 4.152107898 + 3.2 = 7.352107898 u = 7.352107898 Simplifying u = 7.352107898Subproblem 2
u + -3.2 = -4.152107898 Simplifying u + -3.2 = -4.152107898 Reorder the terms: -3.2 + u = -4.152107898 Solving -3.2 + u = -4.152107898 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + u = -4.152107898 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + u = -4.152107898 + 3.2 u = -4.152107898 + 3.2 Combine like terms: -4.152107898 + 3.2 = -0.952107898 u = -0.952107898 Simplifying u = -0.952107898Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.352107898, -0.952107898}
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