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Simplifying -40 = 4.9t(-3.265t + -8.163) Reorder the terms: -40 = 4.9t(-8.163 + -3.265t) -40 = (-8.163 * 4.9t + -3.265t * 4.9t) -40 = (-39.9987t + -15.9985t2) Solving -40 = -39.9987t + -15.9985t2 Solving for variable 't'. Reorder the terms: -40 + 39.9987t + 15.9985t2 = -39.9987t + 39.9987t + -15.9985t2 + 15.9985t2 Combine like terms: -39.9987t + 39.9987t = 0.0000 -40 + 39.9987t + 15.9985t2 = 0.0000 + -15.9985t2 + 15.9985t2 -40 + 39.9987t + 15.9985t2 = -15.9985t2 + 15.9985t2 Combine like terms: -15.9985t2 + 15.9985t2 = 0.0000 -40 + 39.9987t + 15.9985t2 = 0.0000 Begin completing the square. Divide all terms by 15.9985 the coefficient of the squared term: Divide each side by '15.9985'. -2.500234397 + 2.500153139t + t2 = 0 Move the constant term to the right: Add '2.500234397' to each side of the equation. -2.500234397 + 2.500153139t + 2.500234397 + t2 = 0 + 2.500234397 Reorder the terms: -2.500234397 + 2.500234397 + 2.500153139t + t2 = 0 + 2.500234397 Combine like terms: -2.500234397 + 2.500234397 = 0.000000000 0.000000000 + 2.500153139t + t2 = 0 + 2.500234397 2.500153139t + t2 = 0 + 2.500234397 Combine like terms: 0 + 2.500234397 = 2.500234397 2.500153139t + t2 = 2.500234397 The t term is 2.500153139t. Take half its coefficient (1.25007657). Square it (1.562691431) and add it to both sides. Add '1.562691431' to each side of the equation. 2.500153139t + 1.562691431 + t2 = 2.500234397 + 1.562691431 Reorder the terms: 1.562691431 + 2.500153139t + t2 = 2.500234397 + 1.562691431 Combine like terms: 2.500234397 + 1.562691431 = 4.062925828 1.562691431 + 2.500153139t + t2 = 4.062925828 Factor a perfect square on the left side: (t + 1.25007657)(t + 1.25007657) = 4.062925828 Calculate the square root of the right side: 2.015670069 Break this problem into two subproblems by setting (t + 1.25007657) equal to 2.015670069 and -2.015670069.Subproblem 1
t + 1.25007657 = 2.015670069 Simplifying t + 1.25007657 = 2.015670069 Reorder the terms: 1.25007657 + t = 2.015670069 Solving 1.25007657 + t = 2.015670069 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25007657' to each side of the equation. 1.25007657 + -1.25007657 + t = 2.015670069 + -1.25007657 Combine like terms: 1.25007657 + -1.25007657 = 0.00000000 0.00000000 + t = 2.015670069 + -1.25007657 t = 2.015670069 + -1.25007657 Combine like terms: 2.015670069 + -1.25007657 = 0.765593499 t = 0.765593499 Simplifying t = 0.765593499Subproblem 2
t + 1.25007657 = -2.015670069 Simplifying t + 1.25007657 = -2.015670069 Reorder the terms: 1.25007657 + t = -2.015670069 Solving 1.25007657 + t = -2.015670069 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25007657' to each side of the equation. 1.25007657 + -1.25007657 + t = -2.015670069 + -1.25007657 Combine like terms: 1.25007657 + -1.25007657 = 0.00000000 0.00000000 + t = -2.015670069 + -1.25007657 t = -2.015670069 + -1.25007657 Combine like terms: -2.015670069 + -1.25007657 = -3.265746639 t = -3.265746639 Simplifying t = -3.265746639Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.765593499, -3.265746639}
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