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Simplifying 24t + -1t2 = 72 Solving 24t + -1t2 = 72 Solving for variable 't'. Reorder the terms: -72 + 24t + -1t2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + 24t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 72 + -24t + t2 = 0 Move the constant term to the right: Add '-72' to each side of the equation. 72 + -24t + -72 + t2 = 0 + -72 Reorder the terms: 72 + -72 + -24t + t2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -24t + t2 = 0 + -72 -24t + t2 = 0 + -72 Combine like terms: 0 + -72 = -72 -24t + t2 = -72 The t term is -24t. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24t + 144 + t2 = -72 + 144 Reorder the terms: 144 + -24t + t2 = -72 + 144 Combine like terms: -72 + 144 = 72 144 + -24t + t2 = 72 Factor a perfect square on the left side: (t + -12)(t + -12) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (t + -12) equal to 8.485281374 and -8.485281374.Subproblem 1
t + -12 = 8.485281374 Simplifying t + -12 = 8.485281374 Reorder the terms: -12 + t = 8.485281374 Solving -12 + t = 8.485281374 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = 8.485281374 + 12 Combine like terms: -12 + 12 = 0 0 + t = 8.485281374 + 12 t = 8.485281374 + 12 Combine like terms: 8.485281374 + 12 = 20.485281374 t = 20.485281374 Simplifying t = 20.485281374Subproblem 2
t + -12 = -8.485281374 Simplifying t + -12 = -8.485281374 Reorder the terms: -12 + t = -8.485281374 Solving -12 + t = -8.485281374 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = -8.485281374 + 12 Combine like terms: -12 + 12 = 0 0 + t = -8.485281374 + 12 t = -8.485281374 + 12 Combine like terms: -8.485281374 + 12 = 3.514718626 t = 3.514718626 Simplifying t = 3.514718626Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.485281374, 3.514718626}
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