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Simplifying 0 = -9.8t2 + 5t + 15 Reorder the terms: 0 = 15 + 5t + -9.8t2 Solving 0 = 15 + 5t + -9.8t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + -5t + 9.8t2 = 15 + 5t + -9.8t2 + -15 + -5t + 9.8t2 Reorder the terms: -15 + -5t + 9.8t2 = 15 + -15 + 5t + -5t + -9.8t2 + 9.8t2 Combine like terms: 15 + -15 = 0 -15 + -5t + 9.8t2 = 0 + 5t + -5t + -9.8t2 + 9.8t2 -15 + -5t + 9.8t2 = 5t + -5t + -9.8t2 + 9.8t2 Combine like terms: 5t + -5t = 0 -15 + -5t + 9.8t2 = 0 + -9.8t2 + 9.8t2 -15 + -5t + 9.8t2 = -9.8t2 + 9.8t2 Combine like terms: -9.8t2 + 9.8t2 = 0.0 -15 + -5t + 9.8t2 = 0.0 Begin completing the square. Divide all terms by 9.8 the coefficient of the squared term: Divide each side by '9.8'. -1.530612245 + -0.5102040816t + t2 = 0 Move the constant term to the right: Add '1.530612245' to each side of the equation. -1.530612245 + -0.5102040816t + 1.530612245 + t2 = 0 + 1.530612245 Reorder the terms: -1.530612245 + 1.530612245 + -0.5102040816t + t2 = 0 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + -0.5102040816t + t2 = 0 + 1.530612245 -0.5102040816t + t2 = 0 + 1.530612245 Combine like terms: 0 + 1.530612245 = 1.530612245 -0.5102040816t + t2 = 1.530612245 The t term is -0.5102040816t. Take half its coefficient (-0.2551020408). Square it (0.06507705122) and add it to both sides. Add '0.06507705122' to each side of the equation. -0.5102040816t + 0.06507705122 + t2 = 1.530612245 + 0.06507705122 Reorder the terms: 0.06507705122 + -0.5102040816t + t2 = 1.530612245 + 0.06507705122 Combine like terms: 1.530612245 + 0.06507705122 = 1.59568929622 0.06507705122 + -0.5102040816t + t2 = 1.59568929622 Factor a perfect square on the left side: (t + -0.2551020408)(t + -0.2551020408) = 1.59568929622 Calculate the square root of the right side: 1.26320596 Break this problem into two subproblems by setting (t + -0.2551020408) equal to 1.26320596 and -1.26320596.Subproblem 1
t + -0.2551020408 = 1.26320596 Simplifying t + -0.2551020408 = 1.26320596 Reorder the terms: -0.2551020408 + t = 1.26320596 Solving -0.2551020408 + t = 1.26320596 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2551020408' to each side of the equation. -0.2551020408 + 0.2551020408 + t = 1.26320596 + 0.2551020408 Combine like terms: -0.2551020408 + 0.2551020408 = 0.0000000000 0.0000000000 + t = 1.26320596 + 0.2551020408 t = 1.26320596 + 0.2551020408 Combine like terms: 1.26320596 + 0.2551020408 = 1.5183080008 t = 1.5183080008 Simplifying t = 1.5183080008Subproblem 2
t + -0.2551020408 = -1.26320596 Simplifying t + -0.2551020408 = -1.26320596 Reorder the terms: -0.2551020408 + t = -1.26320596 Solving -0.2551020408 + t = -1.26320596 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2551020408' to each side of the equation. -0.2551020408 + 0.2551020408 + t = -1.26320596 + 0.2551020408 Combine like terms: -0.2551020408 + 0.2551020408 = 0.0000000000 0.0000000000 + t = -1.26320596 + 0.2551020408 t = -1.26320596 + 0.2551020408 Combine like terms: -1.26320596 + 0.2551020408 = -1.0081039192 t = -1.0081039192 Simplifying t = -1.0081039192Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.5183080008, -1.0081039192}
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