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Simplifying t2 + -36t + 324 = 85 Reorder the terms: 324 + -36t + t2 = 85 Solving 324 + -36t + t2 = 85 Solving for variable 't'. Reorder the terms: 324 + -85 + -36t + t2 = 85 + -85 Combine like terms: 324 + -85 = 239 239 + -36t + t2 = 85 + -85 Combine like terms: 85 + -85 = 0 239 + -36t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-239' to each side of the equation. 239 + -36t + -239 + t2 = 0 + -239 Reorder the terms: 239 + -239 + -36t + t2 = 0 + -239 Combine like terms: 239 + -239 = 0 0 + -36t + t2 = 0 + -239 -36t + t2 = 0 + -239 Combine like terms: 0 + -239 = -239 -36t + t2 = -239 The t term is -36t. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36t + 324 + t2 = -239 + 324 Reorder the terms: 324 + -36t + t2 = -239 + 324 Combine like terms: -239 + 324 = 85 324 + -36t + t2 = 85 Factor a perfect square on the left side: (t + -18)(t + -18) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (t + -18) equal to 9.219544457 and -9.219544457.Subproblem 1
t + -18 = 9.219544457 Simplifying t + -18 = 9.219544457 Reorder the terms: -18 + t = 9.219544457 Solving -18 + t = 9.219544457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + t = 9.219544457 + 18 Combine like terms: -18 + 18 = 0 0 + t = 9.219544457 + 18 t = 9.219544457 + 18 Combine like terms: 9.219544457 + 18 = 27.219544457 t = 27.219544457 Simplifying t = 27.219544457Subproblem 2
t + -18 = -9.219544457 Simplifying t + -18 = -9.219544457 Reorder the terms: -18 + t = -9.219544457 Solving -18 + t = -9.219544457 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + t = -9.219544457 + 18 Combine like terms: -18 + 18 = 0 0 + t = -9.219544457 + 18 t = -9.219544457 + 18 Combine like terms: -9.219544457 + 18 = 8.780455543 t = 8.780455543 Simplifying t = 8.780455543Solution
The solution to the problem is based on the solutions from the subproblems. t = {27.219544457, 8.780455543}
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