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Simplifying 4u2 + 7u + 2 = 0 Reorder the terms: 2 + 7u + 4u2 = 0 Solving 2 + 7u + 4u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 1.75u + u2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 1.75u + -0.5 + u2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 1.75u + u2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 1.75u + u2 = 0 + -0.5 1.75u + u2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 1.75u + u2 = -0.5 The u term is 1.75u. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75u + 0.765625 + u2 = -0.5 + 0.765625 Reorder the terms: 0.765625 + 1.75u + u2 = -0.5 + 0.765625 Combine like terms: -0.5 + 0.765625 = 0.265625 0.765625 + 1.75u + u2 = 0.265625 Factor a perfect square on the left side: (u + 0.875)(u + 0.875) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (u + 0.875) equal to 0.515388203 and -0.515388203.Subproblem 1
u + 0.875 = 0.515388203 Simplifying u + 0.875 = 0.515388203 Reorder the terms: 0.875 + u = 0.515388203 Solving 0.875 + u = 0.515388203 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + u = 0.515388203 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + u = 0.515388203 + -0.875 u = 0.515388203 + -0.875 Combine like terms: 0.515388203 + -0.875 = -0.359611797 u = -0.359611797 Simplifying u = -0.359611797Subproblem 2
u + 0.875 = -0.515388203 Simplifying u + 0.875 = -0.515388203 Reorder the terms: 0.875 + u = -0.515388203 Solving 0.875 + u = -0.515388203 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + u = -0.515388203 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + u = -0.515388203 + -0.875 u = -0.515388203 + -0.875 Combine like terms: -0.515388203 + -0.875 = -1.390388203 u = -1.390388203 Simplifying u = -1.390388203Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.359611797, -1.390388203}
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