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Simplifying 56u2 + -3305u + 57 = 0 Reorder the terms: 57 + -3305u + 56u2 = 0 Solving 57 + -3305u + 56u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. 1.017857143 + -59.01785714u + u2 = 0 Move the constant term to the right: Add '-1.017857143' to each side of the equation. 1.017857143 + -59.01785714u + -1.017857143 + u2 = 0 + -1.017857143 Reorder the terms: 1.017857143 + -1.017857143 + -59.01785714u + u2 = 0 + -1.017857143 Combine like terms: 1.017857143 + -1.017857143 = 0.000000000 0.000000000 + -59.01785714u + u2 = 0 + -1.017857143 -59.01785714u + u2 = 0 + -1.017857143 Combine like terms: 0 + -1.017857143 = -1.017857143 -59.01785714u + u2 = -1.017857143 The u term is -59.01785714u. Take half its coefficient (-29.50892857). Square it (870.7768653) and add it to both sides. Add '870.7768653' to each side of the equation. -59.01785714u + 870.7768653 + u2 = -1.017857143 + 870.7768653 Reorder the terms: 870.7768653 + -59.01785714u + u2 = -1.017857143 + 870.7768653 Combine like terms: -1.017857143 + 870.7768653 = 869.759008157 870.7768653 + -59.01785714u + u2 = 869.759008157 Factor a perfect square on the left side: (u + -29.50892857)(u + -29.50892857) = 869.759008157 Calculate the square root of the right side: 29.49167693 Break this problem into two subproblems by setting (u + -29.50892857) equal to 29.49167693 and -29.49167693.Subproblem 1
u + -29.50892857 = 29.49167693 Simplifying u + -29.50892857 = 29.49167693 Reorder the terms: -29.50892857 + u = 29.49167693 Solving -29.50892857 + u = 29.49167693 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '29.50892857' to each side of the equation. -29.50892857 + 29.50892857 + u = 29.49167693 + 29.50892857 Combine like terms: -29.50892857 + 29.50892857 = 0.00000000 0.00000000 + u = 29.49167693 + 29.50892857 u = 29.49167693 + 29.50892857 Combine like terms: 29.49167693 + 29.50892857 = 59.0006055 u = 59.0006055 Simplifying u = 59.0006055Subproblem 2
u + -29.50892857 = -29.49167693 Simplifying u + -29.50892857 = -29.49167693 Reorder the terms: -29.50892857 + u = -29.49167693 Solving -29.50892857 + u = -29.49167693 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '29.50892857' to each side of the equation. -29.50892857 + 29.50892857 + u = -29.49167693 + 29.50892857 Combine like terms: -29.50892857 + 29.50892857 = 0.00000000 0.00000000 + u = -29.49167693 + 29.50892857 u = -29.49167693 + 29.50892857 Combine like terms: -29.49167693 + 29.50892857 = 0.01725164 u = 0.01725164 Simplifying u = 0.01725164Solution
The solution to the problem is based on the solutions from the subproblems. u = {59.0006055, 0.01725164}
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