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Simplifying 4u2 + -9u + 4 = 0 Reorder the terms: 4 + -9u + 4u2 = 0 Solving 4 + -9u + 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'. 1 + -2.25u + u2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.25u + -1 + u2 = 0 + -1 Reorder the terms: 1 + -1 + -2.25u + u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.25u + u2 = 0 + -1 -2.25u + u2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.25u + u2 = -1 The u term is -2.25u. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25u + 1.265625 + u2 = -1 + 1.265625 Reorder the terms: 1.265625 + -2.25u + u2 = -1 + 1.265625 Combine like terms: -1 + 1.265625 = 0.265625 1.265625 + -2.25u + u2 = 0.265625 Factor a perfect square on the left side: (u + -1.125)(u + -1.125) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (u + -1.125) equal to 0.515388203 and -0.515388203.Subproblem 1
u + -1.125 = 0.515388203 Simplifying u + -1.125 = 0.515388203 Reorder the terms: -1.125 + u = 0.515388203 Solving -1.125 + u = 0.515388203 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + u = 0.515388203 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + u = 0.515388203 + 1.125 u = 0.515388203 + 1.125 Combine like terms: 0.515388203 + 1.125 = 1.640388203 u = 1.640388203 Simplifying u = 1.640388203Subproblem 2
u + -1.125 = -0.515388203 Simplifying u + -1.125 = -0.515388203 Reorder the terms: -1.125 + u = -0.515388203 Solving -1.125 + u = -0.515388203 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + u = -0.515388203 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + u = -0.515388203 + 1.125 u = -0.515388203 + 1.125 Combine like terms: -0.515388203 + 1.125 = 0.609611797 u = 0.609611797 Simplifying u = 0.609611797Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.640388203, 0.609611797}
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