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Simplifying 0 = -16t2 + 215t + 40 Reorder the terms: 0 = 40 + 215t + -16t2 Solving 0 = 40 + 215t + -16t2 Solving for variable 't'. Combine like terms: 0 + -40 = -40 -40 + -215t + 16t2 = 40 + 215t + -16t2 + -40 + -215t + 16t2 Reorder the terms: -40 + -215t + 16t2 = 40 + -40 + 215t + -215t + -16t2 + 16t2 Combine like terms: 40 + -40 = 0 -40 + -215t + 16t2 = 0 + 215t + -215t + -16t2 + 16t2 -40 + -215t + 16t2 = 215t + -215t + -16t2 + 16t2 Combine like terms: 215t + -215t = 0 -40 + -215t + 16t2 = 0 + -16t2 + 16t2 -40 + -215t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -40 + -215t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.5 + -13.4375t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -13.4375t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -13.4375t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -13.4375t + t2 = 0 + 2.5 -13.4375t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -13.4375t + t2 = 2.5 The t term is -13.4375t. Take half its coefficient (-6.71875). Square it (45.14160156) and add it to both sides. Add '45.14160156' to each side of the equation. -13.4375t + 45.14160156 + t2 = 2.5 + 45.14160156 Reorder the terms: 45.14160156 + -13.4375t + t2 = 2.5 + 45.14160156 Combine like terms: 2.5 + 45.14160156 = 47.64160156 45.14160156 + -13.4375t + t2 = 47.64160156 Factor a perfect square on the left side: (t + -6.71875)(t + -6.71875) = 47.64160156 Calculate the square root of the right side: 6.902289588 Break this problem into two subproblems by setting (t + -6.71875) equal to 6.902289588 and -6.902289588.Subproblem 1
t + -6.71875 = 6.902289588 Simplifying t + -6.71875 = 6.902289588 Reorder the terms: -6.71875 + t = 6.902289588 Solving -6.71875 + t = 6.902289588 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.71875' to each side of the equation. -6.71875 + 6.71875 + t = 6.902289588 + 6.71875 Combine like terms: -6.71875 + 6.71875 = 0.00000 0.00000 + t = 6.902289588 + 6.71875 t = 6.902289588 + 6.71875 Combine like terms: 6.902289588 + 6.71875 = 13.621039588 t = 13.621039588 Simplifying t = 13.621039588Subproblem 2
t + -6.71875 = -6.902289588 Simplifying t + -6.71875 = -6.902289588 Reorder the terms: -6.71875 + t = -6.902289588 Solving -6.71875 + t = -6.902289588 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.71875' to each side of the equation. -6.71875 + 6.71875 + t = -6.902289588 + 6.71875 Combine like terms: -6.71875 + 6.71875 = 0.00000 0.00000 + t = -6.902289588 + 6.71875 t = -6.902289588 + 6.71875 Combine like terms: -6.902289588 + 6.71875 = -0.183539588 t = -0.183539588 Simplifying t = -0.183539588Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.621039588, -0.183539588}
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