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Simplifying 19.6 = 24.5t + -4.9t2 Solving 19.6 = 24.5t + -4.9t2 Solving for variable 't'. Reorder the terms: 19.6 + -24.5t + 4.9t2 = 24.5t + -24.5t + -4.9t2 + 4.9t2 Combine like terms: 24.5t + -24.5t = 0.0 19.6 + -24.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 19.6 + -24.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 19.6 + -24.5t + 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'. 4 + -5t + t2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -5t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + -5t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5t + t2 = 0 + -4 -5t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 -5t + t2 = -4 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -4 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -4 + 6.25 Combine like terms: -4 + 6.25 = 2.25 6.25 + -5t + t2 = 2.25 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (t + -2.5) equal to 1.5 and -1.5.Subproblem 1
t + -2.5 = 1.5 Simplifying t + -2.5 = 1.5 Reorder the terms: -2.5 + t = 1.5 Solving -2.5 + t = 1.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 1.5 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 1.5 + 2.5 t = 1.5 + 2.5 Combine like terms: 1.5 + 2.5 = 4 t = 4 Simplifying t = 4Subproblem 2
t + -2.5 = -1.5 Simplifying t + -2.5 = -1.5 Reorder the terms: -2.5 + t = -1.5 Solving -2.5 + t = -1.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -1.5 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -1.5 + 2.5 t = -1.5 + 2.5 Combine like terms: -1.5 + 2.5 = 1 t = 1 Simplifying t = 1Solution
The solution to the problem is based on the solutions from the subproblems. t = {4, 1}
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