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Simplifying 0 = -0.75t2 + 363t + -36720 Reorder the terms: 0 = -36720 + 363t + -0.75t2 Solving 0 = -36720 + 363t + -0.75t2 Solving for variable 't'. Combine like terms: 0 + 36720 = 36720 36720 + -363t + 0.75t2 = -36720 + 363t + -0.75t2 + 36720 + -363t + 0.75t2 Reorder the terms: 36720 + -363t + 0.75t2 = -36720 + 36720 + 363t + -363t + -0.75t2 + 0.75t2 Combine like terms: -36720 + 36720 = 0 36720 + -363t + 0.75t2 = 0 + 363t + -363t + -0.75t2 + 0.75t2 36720 + -363t + 0.75t2 = 363t + -363t + -0.75t2 + 0.75t2 Combine like terms: 363t + -363t = 0 36720 + -363t + 0.75t2 = 0 + -0.75t2 + 0.75t2 36720 + -363t + 0.75t2 = -0.75t2 + 0.75t2 Combine like terms: -0.75t2 + 0.75t2 = 0.00 36720 + -363t + 0.75t2 = 0.00 Begin completing the square. Divide all terms by 0.75 the coefficient of the squared term: Divide each side by '0.75'. 48960 + -484t + t2 = 0 Move the constant term to the right: Add '-48960' to each side of the equation. 48960 + -484t + -48960 + t2 = 0 + -48960 Reorder the terms: 48960 + -48960 + -484t + t2 = 0 + -48960 Combine like terms: 48960 + -48960 = 0 0 + -484t + t2 = 0 + -48960 -484t + t2 = 0 + -48960 Combine like terms: 0 + -48960 = -48960 -484t + t2 = -48960 The t term is -484t. Take half its coefficient (-242). Square it (58564) and add it to both sides. Add '58564' to each side of the equation. -484t + 58564 + t2 = -48960 + 58564 Reorder the terms: 58564 + -484t + t2 = -48960 + 58564 Combine like terms: -48960 + 58564 = 9604 58564 + -484t + t2 = 9604 Factor a perfect square on the left side: (t + -242)(t + -242) = 9604 Calculate the square root of the right side: 98 Break this problem into two subproblems by setting (t + -242) equal to 98 and -98.Subproblem 1
t + -242 = 98 Simplifying t + -242 = 98 Reorder the terms: -242 + t = 98 Solving -242 + t = 98 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '242' to each side of the equation. -242 + 242 + t = 98 + 242 Combine like terms: -242 + 242 = 0 0 + t = 98 + 242 t = 98 + 242 Combine like terms: 98 + 242 = 340 t = 340 Simplifying t = 340Subproblem 2
t + -242 = -98 Simplifying t + -242 = -98 Reorder the terms: -242 + t = -98 Solving -242 + t = -98 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '242' to each side of the equation. -242 + 242 + t = -98 + 242 Combine like terms: -242 + 242 = 0 0 + t = -98 + 242 t = -98 + 242 Combine like terms: -98 + 242 = 144 t = 144 Simplifying t = 144Solution
The solution to the problem is based on the solutions from the subproblems. t = {340, 144}
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