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Simplifying 1 = 12t + 0.5t2 Solving 1 = 12t + 0.5t2 Solving for variable 't'. Reorder the terms: 1 + -12t + -0.5t2 = 12t + -12t + 0.5t2 + -0.5t2 Combine like terms: 12t + -12t = 0 1 + -12t + -0.5t2 = 0 + 0.5t2 + -0.5t2 1 + -12t + -0.5t2 = 0.5t2 + -0.5t2 Combine like terms: 0.5t2 + -0.5t2 = 0.0 1 + -12t + -0.5t2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -2 + 24t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 24t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + 24t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 24t + t2 = 0 + 2 24t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 24t + t2 = 2 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 = 2 + 144 Reorder the terms: 144 + 24t + t2 = 2 + 144 Combine like terms: 2 + 144 = 146 144 + 24t + t2 = 146 Factor a perfect square on the left side: (t + 12)(t + 12) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (t + 12) equal to 12.083045974 and -12.083045974.Subproblem 1
t + 12 = 12.083045974 Simplifying t + 12 = 12.083045974 Reorder the terms: 12 + t = 12.083045974 Solving 12 + t = 12.083045974 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 = 12.083045974 + -12 Combine like terms: 12 + -12 = 0 0 + t = 12.083045974 + -12 t = 12.083045974 + -12 Combine like terms: 12.083045974 + -12 = 0.083045974 t = 0.083045974 Simplifying t = 0.083045974Subproblem 2
t + 12 = -12.083045974 Simplifying t + 12 = -12.083045974 Reorder the terms: 12 + t = -12.083045974 Solving 12 + t = -12.083045974 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 = -12.083045974 + -12 Combine like terms: 12 + -12 = 0 0 + t = -12.083045974 + -12 t = -12.083045974 + -12 Combine like terms: -12.083045974 + -12 = -24.083045974 t = -24.083045974 Simplifying t = -24.083045974Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.083045974, -24.083045974}
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