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Simplifying t2 + -24.5t + 2 = 0 Reorder the terms: 2 + -24.5t + t2 = 0 Solving 2 + -24.5t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -24.5t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + -24.5t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -24.5t + t2 = 0 + -2 -24.5t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -24.5t + t2 = -2 The t term is -24.5t. Take half its coefficient (-12.25). Square it (150.0625) and add it to both sides. Add '150.0625' to each side of the equation. -24.5t + 150.0625 + t2 = -2 + 150.0625 Reorder the terms: 150.0625 + -24.5t + t2 = -2 + 150.0625 Combine like terms: -2 + 150.0625 = 148.0625 150.0625 + -24.5t + t2 = 148.0625 Factor a perfect square on the left side: (t + -12.25)(t + -12.25) = 148.0625 Calculate the square root of the right side: 12.168093524 Break this problem into two subproblems by setting (t + -12.25) equal to 12.168093524 and -12.168093524.Subproblem 1
t + -12.25 = 12.168093524 Simplifying t + -12.25 = 12.168093524 Reorder the terms: -12.25 + t = 12.168093524 Solving -12.25 + t = 12.168093524 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.25' to each side of the equation. -12.25 + 12.25 + t = 12.168093524 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + t = 12.168093524 + 12.25 t = 12.168093524 + 12.25 Combine like terms: 12.168093524 + 12.25 = 24.418093524 t = 24.418093524 Simplifying t = 24.418093524Subproblem 2
t + -12.25 = -12.168093524 Simplifying t + -12.25 = -12.168093524 Reorder the terms: -12.25 + t = -12.168093524 Solving -12.25 + t = -12.168093524 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.25' to each side of the equation. -12.25 + 12.25 + t = -12.168093524 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + t = -12.168093524 + 12.25 t = -12.168093524 + 12.25 Combine like terms: -12.168093524 + 12.25 = 0.081906476 t = 0.081906476 Simplifying t = 0.081906476Solution
The solution to the problem is based on the solutions from the subproblems. t = {24.418093524, 0.081906476}
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