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Simplifying t2 + -24t + 81 = 0 Reorder the terms: 81 + -24t + t2 = 0 Solving 81 + -24t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + -24t + -81 + t2 = 0 + -81 Reorder the terms: 81 + -81 + -24t + t2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + -24t + t2 = 0 + -81 -24t + t2 = 0 + -81 Combine like terms: 0 + -81 = -81 -24t + t2 = -81 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 = -81 + 144 Reorder the terms: 144 + -24t + t2 = -81 + 144 Combine like terms: -81 + 144 = 63 144 + -24t + t2 = 63 Factor a perfect square on the left side: (t + -12)(t + -12) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (t + -12) equal to 7.937253933 and -7.937253933.Subproblem 1
t + -12 = 7.937253933 Simplifying t + -12 = 7.937253933 Reorder the terms: -12 + t = 7.937253933 Solving -12 + t = 7.937253933 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 = 7.937253933 + 12 Combine like terms: -12 + 12 = 0 0 + t = 7.937253933 + 12 t = 7.937253933 + 12 Combine like terms: 7.937253933 + 12 = 19.937253933 t = 19.937253933 Simplifying t = 19.937253933Subproblem 2
t + -12 = -7.937253933 Simplifying t + -12 = -7.937253933 Reorder the terms: -12 + t = -7.937253933 Solving -12 + t = -7.937253933 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 = -7.937253933 + 12 Combine like terms: -12 + 12 = 0 0 + t = -7.937253933 + 12 t = -7.937253933 + 12 Combine like terms: -7.937253933 + 12 = 4.062746067 t = 4.062746067 Simplifying t = 4.062746067Solution
The solution to the problem is based on the solutions from the subproblems. t = {19.937253933, 4.062746067}
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