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Simplifying 9.8 = -490t2 + 1470t Reorder the terms: 9.8 = 1470t + -490t2 Solving 9.8 = 1470t + -490t2 Solving for variable 't'. Reorder the terms: 9.8 + -1470t + 490t2 = 1470t + -1470t + -490t2 + 490t2 Combine like terms: 1470t + -1470t = 0 9.8 + -1470t + 490t2 = 0 + -490t2 + 490t2 9.8 + -1470t + 490t2 = -490t2 + 490t2 Combine like terms: -490t2 + 490t2 = 0 9.8 + -1470t + 490t2 = 0 Begin completing the square. Divide all terms by 490 the coefficient of the squared term: Divide each side by '490'. 0.02 + -3t + t2 = 0 Move the constant term to the right: Add '-0.02' to each side of the equation. 0.02 + -3t + -0.02 + t2 = 0 + -0.02 Reorder the terms: 0.02 + -0.02 + -3t + t2 = 0 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + -3t + t2 = 0 + -0.02 -3t + t2 = 0 + -0.02 Combine like terms: 0 + -0.02 = -0.02 -3t + t2 = -0.02 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = -0.02 + 2.25 Reorder the terms: 2.25 + -3t + t2 = -0.02 + 2.25 Combine like terms: -0.02 + 2.25 = 2.23 2.25 + -3t + t2 = 2.23 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 2.23 Calculate the square root of the right side: 1.493318452 Break this problem into two subproblems by setting (t + -1.5) equal to 1.493318452 and -1.493318452.Subproblem 1
t + -1.5 = 1.493318452 Simplifying t + -1.5 = 1.493318452 Reorder the terms: -1.5 + t = 1.493318452 Solving -1.5 + t = 1.493318452 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 1.493318452 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 1.493318452 + 1.5 t = 1.493318452 + 1.5 Combine like terms: 1.493318452 + 1.5 = 2.993318452 t = 2.993318452 Simplifying t = 2.993318452Subproblem 2
t + -1.5 = -1.493318452 Simplifying t + -1.5 = -1.493318452 Reorder the terms: -1.5 + t = -1.493318452 Solving -1.5 + t = -1.493318452 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -1.493318452 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -1.493318452 + 1.5 t = -1.493318452 + 1.5 Combine like terms: -1.493318452 + 1.5 = 0.006681548 t = 0.006681548 Simplifying t = 0.006681548Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.993318452, 0.006681548}
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