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Simplifying 75 = 25t + 0.5 * 9.8t2 Multiply 0.5 * 9.8 75 = 25t + 4.9t2 Solving 75 = 25t + 4.9t2 Solving for variable 't'. Reorder the terms: 75 + -25t + -4.9t2 = 25t + -25t + 4.9t2 + -4.9t2 Combine like terms: 25t + -25t = 0 75 + -25t + -4.9t2 = 0 + 4.9t2 + -4.9t2 75 + -25t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 75 + -25t + -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'. -15.30612245 + 5.102040816t + t2 = 0 Move the constant term to the right: Add '15.30612245' to each side of the equation. -15.30612245 + 5.102040816t + 15.30612245 + t2 = 0 + 15.30612245 Reorder the terms: -15.30612245 + 15.30612245 + 5.102040816t + t2 = 0 + 15.30612245 Combine like terms: -15.30612245 + 15.30612245 = 0.00000000 0.00000000 + 5.102040816t + t2 = 0 + 15.30612245 5.102040816t + t2 = 0 + 15.30612245 Combine like terms: 0 + 15.30612245 = 15.30612245 5.102040816t + t2 = 15.30612245 The t term is 5.102040816t. Take half its coefficient (2.551020408). Square it (6.507705122) and add it to both sides. Add '6.507705122' to each side of the equation. 5.102040816t + 6.507705122 + t2 = 15.30612245 + 6.507705122 Reorder the terms: 6.507705122 + 5.102040816t + t2 = 15.30612245 + 6.507705122 Combine like terms: 15.30612245 + 6.507705122 = 21.813827572 6.507705122 + 5.102040816t + t2 = 21.813827572 Factor a perfect square on the left side: (t + 2.551020408)(t + 2.551020408) = 21.813827572 Calculate the square root of the right side: 4.670527548 Break this problem into two subproblems by setting (t + 2.551020408) equal to 4.670527548 and -4.670527548.Subproblem 1
t + 2.551020408 = 4.670527548 Simplifying t + 2.551020408 = 4.670527548 Reorder the terms: 2.551020408 + t = 4.670527548 Solving 2.551020408 + t = 4.670527548 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.551020408' to each side of the equation. 2.551020408 + -2.551020408 + t = 4.670527548 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = 4.670527548 + -2.551020408 t = 4.670527548 + -2.551020408 Combine like terms: 4.670527548 + -2.551020408 = 2.11950714 t = 2.11950714 Simplifying t = 2.11950714Subproblem 2
t + 2.551020408 = -4.670527548 Simplifying t + 2.551020408 = -4.670527548 Reorder the terms: 2.551020408 + t = -4.670527548 Solving 2.551020408 + t = -4.670527548 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.551020408' to each side of the equation. 2.551020408 + -2.551020408 + t = -4.670527548 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = -4.670527548 + -2.551020408 t = -4.670527548 + -2.551020408 Combine like terms: -4.670527548 + -2.551020408 = -7.221547956 t = -7.221547956 Simplifying t = -7.221547956Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.11950714, -7.221547956}
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