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Simplifying 1960 = 4.9t(50 + -1t) 1960 = (50 * 4.9t + -1t * 4.9t) 1960 = (245t + -4.9t2) Solving 1960 = 245t + -4.9t2 Solving for variable 't'. Reorder the terms: 1960 + -245t + 4.9t2 = 245t + -245t + -4.9t2 + 4.9t2 Combine like terms: 245t + -245t = 0 1960 + -245t + 4.9t2 = 0 + -4.9t2 + 4.9t2 1960 + -245t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 1960 + -245t + 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'. 400 + -50t + t2 = 0 Move the constant term to the right: Add '-400' to each side of the equation. 400 + -50t + -400 + t2 = 0 + -400 Reorder the terms: 400 + -400 + -50t + t2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -50t + t2 = 0 + -400 -50t + t2 = 0 + -400 Combine like terms: 0 + -400 = -400 -50t + t2 = -400 The t term is -50t. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50t + 625 + t2 = -400 + 625 Reorder the terms: 625 + -50t + t2 = -400 + 625 Combine like terms: -400 + 625 = 225 625 + -50t + t2 = 225 Factor a perfect square on the left side: (t + -25)(t + -25) = 225 Calculate the square root of the right side: 15 Break this problem into two subproblems by setting (t + -25) equal to 15 and -15.Subproblem 1
t + -25 = 15 Simplifying t + -25 = 15 Reorder the terms: -25 + t = 15 Solving -25 + t = 15 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t = 15 + 25 Combine like terms: -25 + 25 = 0 0 + t = 15 + 25 t = 15 + 25 Combine like terms: 15 + 25 = 40 t = 40 Simplifying t = 40Subproblem 2
t + -25 = -15 Simplifying t + -25 = -15 Reorder the terms: -25 + t = -15 Solving -25 + t = -15 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + t = -15 + 25 Combine like terms: -25 + 25 = 0 0 + t = -15 + 25 t = -15 + 25 Combine like terms: -15 + 25 = 10 t = 10 Simplifying t = 10Solution
The solution to the problem is based on the solutions from the subproblems. t = {40, 10}
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