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Simplifying 3u + 4 = 5u2 Reorder the terms: 4 + 3u = 5u2 Solving 4 + 3u = 5u2 Solving for variable 'u'. Combine like terms: 5u2 + -5u2 = 0 4 + 3u + -5u2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.8 + -0.6u + u2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.6u + 0.8 + u2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.6u + u2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.6u + u2 = 0 + 0.8 -0.6u + u2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.6u + u2 = 0.8 The u term is -0.6u. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6u + 0.09 + u2 = 0.8 + 0.09 Reorder the terms: 0.09 + -0.6u + u2 = 0.8 + 0.09 Combine like terms: 0.8 + 0.09 = 0.89 0.09 + -0.6u + u2 = 0.89 Factor a perfect square on the left side: (u + -0.3)(u + -0.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (u + -0.3) equal to 0.943398113 and -0.943398113.Subproblem 1
u + -0.3 = 0.943398113 Simplifying u + -0.3 = 0.943398113 Reorder the terms: -0.3 + u = 0.943398113 Solving -0.3 + u = 0.943398113 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + u = 0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + u = 0.943398113 + 0.3 u = 0.943398113 + 0.3 Combine like terms: 0.943398113 + 0.3 = 1.243398113 u = 1.243398113 Simplifying u = 1.243398113Subproblem 2
u + -0.3 = -0.943398113 Simplifying u + -0.3 = -0.943398113 Reorder the terms: -0.3 + u = -0.943398113 Solving -0.3 + u = -0.943398113 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + u = -0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + u = -0.943398113 + 0.3 u = -0.943398113 + 0.3 Combine like terms: -0.943398113 + 0.3 = -0.643398113 u = -0.643398113 Simplifying u = -0.643398113Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.243398113, -0.643398113}
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