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Simplifying t2 + -24t = 135 Reorder the terms: -24t + t2 = 135 Solving -24t + t2 = 135 Solving for variable 't'. Reorder the terms: -135 + -24t + t2 = 135 + -135 Combine like terms: 135 + -135 = 0 -135 + -24t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '135' to each side of the equation. -135 + -24t + 135 + t2 = 0 + 135 Reorder the terms: -135 + 135 + -24t + t2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + -24t + t2 = 0 + 135 -24t + t2 = 0 + 135 Combine like terms: 0 + 135 = 135 -24t + t2 = 135 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 = 135 + 144 Reorder the terms: 144 + -24t + t2 = 135 + 144 Combine like terms: 135 + 144 = 279 144 + -24t + t2 = 279 Factor a perfect square on the left side: (t + -12)(t + -12) = 279 Calculate the square root of the right side: 16.703293088 Break this problem into two subproblems by setting (t + -12) equal to 16.703293088 and -16.703293088.Subproblem 1
t + -12 = 16.703293088 Simplifying t + -12 = 16.703293088 Reorder the terms: -12 + t = 16.703293088 Solving -12 + t = 16.703293088 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 = 16.703293088 + 12 Combine like terms: -12 + 12 = 0 0 + t = 16.703293088 + 12 t = 16.703293088 + 12 Combine like terms: 16.703293088 + 12 = 28.703293088 t = 28.703293088 Simplifying t = 28.703293088Subproblem 2
t + -12 = -16.703293088 Simplifying t + -12 = -16.703293088 Reorder the terms: -12 + t = -16.703293088 Solving -12 + t = -16.703293088 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 = -16.703293088 + 12 Combine like terms: -12 + 12 = 0 0 + t = -16.703293088 + 12 t = -16.703293088 + 12 Combine like terms: -16.703293088 + 12 = -4.703293088 t = -4.703293088 Simplifying t = -4.703293088Solution
The solution to the problem is based on the solutions from the subproblems. t = {28.703293088, -4.703293088}
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