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Simplifying -4.9t2 + 121t + 262 = 0 Reorder the terms: 262 + 121t + -4.9t2 = 0 Solving 262 + 121t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -53.46938776 + -24.69387755t + t2 = 0 Move the constant term to the right: Add '53.46938776' to each side of the equation. -53.46938776 + -24.69387755t + 53.46938776 + t2 = 0 + 53.46938776 Reorder the terms: -53.46938776 + 53.46938776 + -24.69387755t + t2 = 0 + 53.46938776 Combine like terms: -53.46938776 + 53.46938776 = 0.00000000 0.00000000 + -24.69387755t + t2 = 0 + 53.46938776 -24.69387755t + t2 = 0 + 53.46938776 Combine like terms: 0 + 53.46938776 = 53.46938776 -24.69387755t + t2 = 53.46938776 The t term is -24.69387755t. Take half its coefficient (-12.34693878). Square it (152.4468972) and add it to both sides. Add '152.4468972' to each side of the equation. -24.69387755t + 152.4468972 + t2 = 53.46938776 + 152.4468972 Reorder the terms: 152.4468972 + -24.69387755t + t2 = 53.46938776 + 152.4468972 Combine like terms: 53.46938776 + 152.4468972 = 205.91628496 152.4468972 + -24.69387755t + t2 = 205.91628496 Factor a perfect square on the left side: (t + -12.34693878)(t + -12.34693878) = 205.91628496 Calculate the square root of the right side: 14.349783446 Break this problem into two subproblems by setting (t + -12.34693878) equal to 14.349783446 and -14.349783446.Subproblem 1
t + -12.34693878 = 14.349783446 Simplifying t + -12.34693878 = 14.349783446 Reorder the terms: -12.34693878 + t = 14.349783446 Solving -12.34693878 + t = 14.349783446 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.34693878' to each side of the equation. -12.34693878 + 12.34693878 + t = 14.349783446 + 12.34693878 Combine like terms: -12.34693878 + 12.34693878 = 0.00000000 0.00000000 + t = 14.349783446 + 12.34693878 t = 14.349783446 + 12.34693878 Combine like terms: 14.349783446 + 12.34693878 = 26.696722226 t = 26.696722226 Simplifying t = 26.696722226Subproblem 2
t + -12.34693878 = -14.349783446 Simplifying t + -12.34693878 = -14.349783446 Reorder the terms: -12.34693878 + t = -14.349783446 Solving -12.34693878 + t = -14.349783446 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.34693878' to each side of the equation. -12.34693878 + 12.34693878 + t = -14.349783446 + 12.34693878 Combine like terms: -12.34693878 + 12.34693878 = 0.00000000 0.00000000 + t = -14.349783446 + 12.34693878 t = -14.349783446 + 12.34693878 Combine like terms: -14.349783446 + 12.34693878 = -2.002844666 t = -2.002844666 Simplifying t = -2.002844666Solution
The solution to the problem is based on the solutions from the subproblems. t = {26.696722226, -2.002844666}
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