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Simplifying t2 + -18t + 60.75 = 0 Reorder the terms: 60.75 + -18t + t2 = 0 Solving 60.75 + -18t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-60.75' to each side of the equation. 60.75 + -18t + -60.75 + t2 = 0 + -60.75 Reorder the terms: 60.75 + -60.75 + -18t + t2 = 0 + -60.75 Combine like terms: 60.75 + -60.75 = 0.00 0.00 + -18t + t2 = 0 + -60.75 -18t + t2 = 0 + -60.75 Combine like terms: 0 + -60.75 = -60.75 -18t + t2 = -60.75 The t term is -18t. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18t + 81 + t2 = -60.75 + 81 Reorder the terms: 81 + -18t + t2 = -60.75 + 81 Combine like terms: -60.75 + 81 = 20.25 81 + -18t + t2 = 20.25 Factor a perfect square on the left side: (t + -9)(t + -9) = 20.25 Calculate the square root of the right side: 4.5 Break this problem into two subproblems by setting (t + -9) equal to 4.5 and -4.5.Subproblem 1
t + -9 = 4.5 Simplifying t + -9 = 4.5 Reorder the terms: -9 + t = 4.5 Solving -9 + t = 4.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 4.5 + 9 Combine like terms: -9 + 9 = 0 0 + t = 4.5 + 9 t = 4.5 + 9 Combine like terms: 4.5 + 9 = 13.5 t = 13.5 Simplifying t = 13.5Subproblem 2
t + -9 = -4.5 Simplifying t + -9 = -4.5 Reorder the terms: -9 + t = -4.5 Solving -9 + t = -4.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = -4.5 + 9 Combine like terms: -9 + 9 = 0 0 + t = -4.5 + 9 t = -4.5 + 9 Combine like terms: -4.5 + 9 = 4.5 t = 4.5 Simplifying t = 4.5Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.5, 4.5}
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