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Simplifying 80 = -4.9t2 + 164t + 30 Reorder the terms: 80 = 30 + 164t + -4.9t2 Solving 80 = 30 + 164t + -4.9t2 Solving for variable 't'. Combine like terms: 80 + -30 = 50 50 + -164t + 4.9t2 = 30 + 164t + -4.9t2 + -30 + -164t + 4.9t2 Reorder the terms: 50 + -164t + 4.9t2 = 30 + -30 + 164t + -164t + -4.9t2 + 4.9t2 Combine like terms: 30 + -30 = 0 50 + -164t + 4.9t2 = 0 + 164t + -164t + -4.9t2 + 4.9t2 50 + -164t + 4.9t2 = 164t + -164t + -4.9t2 + 4.9t2 Combine like terms: 164t + -164t = 0 50 + -164t + 4.9t2 = 0 + -4.9t2 + 4.9t2 50 + -164t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 50 + -164t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 10.20408163 + -33.46938776t + t2 = 0 Move the constant term to the right: Add '-10.20408163' to each side of the equation. 10.20408163 + -33.46938776t + -10.20408163 + t2 = 0 + -10.20408163 Reorder the terms: 10.20408163 + -10.20408163 + -33.46938776t + t2 = 0 + -10.20408163 Combine like terms: 10.20408163 + -10.20408163 = 0.00000000 0.00000000 + -33.46938776t + t2 = 0 + -10.20408163 -33.46938776t + t2 = 0 + -10.20408163 Combine like terms: 0 + -10.20408163 = -10.20408163 -33.46938776t + t2 = -10.20408163 The t term is -33.46938776t. Take half its coefficient (-16.73469388). Square it (280.0499793) and add it to both sides. Add '280.0499793' to each side of the equation. -33.46938776t + 280.0499793 + t2 = -10.20408163 + 280.0499793 Reorder the terms: 280.0499793 + -33.46938776t + t2 = -10.20408163 + 280.0499793 Combine like terms: -10.20408163 + 280.0499793 = 269.84589767 280.0499793 + -33.46938776t + t2 = 269.84589767 Factor a perfect square on the left side: (t + -16.73469388)(t + -16.73469388) = 269.84589767 Calculate the square root of the right side: 16.426986871 Break this problem into two subproblems by setting (t + -16.73469388) equal to 16.426986871 and -16.426986871.Subproblem 1
t + -16.73469388 = 16.426986871 Simplifying t + -16.73469388 = 16.426986871 Reorder the terms: -16.73469388 + t = 16.426986871 Solving -16.73469388 + t = 16.426986871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '16.73469388' to each side of the equation. -16.73469388 + 16.73469388 + t = 16.426986871 + 16.73469388 Combine like terms: -16.73469388 + 16.73469388 = 0.00000000 0.00000000 + t = 16.426986871 + 16.73469388 t = 16.426986871 + 16.73469388 Combine like terms: 16.426986871 + 16.73469388 = 33.161680751 t = 33.161680751 Simplifying t = 33.161680751Subproblem 2
t + -16.73469388 = -16.426986871 Simplifying t + -16.73469388 = -16.426986871 Reorder the terms: -16.73469388 + t = -16.426986871 Solving -16.73469388 + t = -16.426986871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '16.73469388' to each side of the equation. -16.73469388 + 16.73469388 + t = -16.426986871 + 16.73469388 Combine like terms: -16.73469388 + 16.73469388 = 0.00000000 0.00000000 + t = -16.426986871 + 16.73469388 t = -16.426986871 + 16.73469388 Combine like terms: -16.426986871 + 16.73469388 = 0.307707009 t = 0.307707009 Simplifying t = 0.307707009Solution
The solution to the problem is based on the solutions from the subproblems. t = {33.161680751, 0.307707009}
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