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Simplifying 18u2 + -3u = 4 Reorder the terms: -3u + 18u2 = 4 Solving -3u + 18u2 = 4 Solving for variable 'u'. Reorder the terms: -4 + -3u + 18u2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -3u + 18u2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2222222222 + -0.1666666667u + u2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -0.1666666667u + 0.2222222222 + u2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -0.1666666667u + u2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -0.1666666667u + u2 = 0 + 0.2222222222 -0.1666666667u + u2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -0.1666666667u + u2 = 0.2222222222 The u term is -0.1666666667u. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667u + 0.006944444447 + u2 = 0.2222222222 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667u + u2 = 0.2222222222 + 0.006944444447 Combine like terms: 0.2222222222 + 0.006944444447 = 0.229166666647 0.006944444447 + -0.1666666667u + u2 = 0.229166666647 Factor a perfect square on the left side: (u + -0.08333333335)(u + -0.08333333335) = 0.229166666647 Calculate the square root of the right side: 0.478713554 Break this problem into two subproblems by setting (u + -0.08333333335) equal to 0.478713554 and -0.478713554.Subproblem 1
u + -0.08333333335 = 0.478713554 Simplifying u + -0.08333333335 = 0.478713554 Reorder the terms: -0.08333333335 + u = 0.478713554 Solving -0.08333333335 + u = 0.478713554 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + u = 0.478713554 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + u = 0.478713554 + 0.08333333335 u = 0.478713554 + 0.08333333335 Combine like terms: 0.478713554 + 0.08333333335 = 0.56204688735 u = 0.56204688735 Simplifying u = 0.56204688735Subproblem 2
u + -0.08333333335 = -0.478713554 Simplifying u + -0.08333333335 = -0.478713554 Reorder the terms: -0.08333333335 + u = -0.478713554 Solving -0.08333333335 + u = -0.478713554 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + u = -0.478713554 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + u = -0.478713554 + 0.08333333335 u = -0.478713554 + 0.08333333335 Combine like terms: -0.478713554 + 0.08333333335 = -0.39538022065 u = -0.39538022065 Simplifying u = -0.39538022065Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.56204688735, -0.39538022065}
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