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Simplifying (t2) + -1(24t) + 96 = 0 t2 + -1(24t) + 96 = 0 Remove parenthesis around (24t) t2 + -1 * 24t + 96 = 0 Multiply -1 * 24 t2 + -24t + 96 = 0 Reorder the terms: 96 + -24t + t2 = 0 Solving 96 + -24t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-96' to each side of the equation. 96 + -24t + -96 + t2 = 0 + -96 Reorder the terms: 96 + -96 + -24t + t2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + -24t + t2 = 0 + -96 -24t + t2 = 0 + -96 Combine like terms: 0 + -96 = -96 -24t + t2 = -96 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 = -96 + 144 Reorder the terms: 144 + -24t + t2 = -96 + 144 Combine like terms: -96 + 144 = 48 144 + -24t + t2 = 48 Factor a perfect square on the left side: (t + -12)(t + -12) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (t + -12) equal to 6.92820323 and -6.92820323.Subproblem 1
t + -12 = 6.92820323 Simplifying t + -12 = 6.92820323 Reorder the terms: -12 + t = 6.92820323 Solving -12 + t = 6.92820323 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 = 6.92820323 + 12 Combine like terms: -12 + 12 = 0 0 + t = 6.92820323 + 12 t = 6.92820323 + 12 Combine like terms: 6.92820323 + 12 = 18.92820323 t = 18.92820323 Simplifying t = 18.92820323Subproblem 2
t + -12 = -6.92820323 Simplifying t + -12 = -6.92820323 Reorder the terms: -12 + t = -6.92820323 Solving -12 + t = -6.92820323 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 = -6.92820323 + 12 Combine like terms: -12 + 12 = 0 0 + t = -6.92820323 + 12 t = -6.92820323 + 12 Combine like terms: -6.92820323 + 12 = 5.07179677 t = 5.07179677 Simplifying t = 5.07179677Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.92820323, 5.07179677}
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