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Simplifying 28 = t(25 + 4.9t) 28 = (25 * t + 4.9t * t) 28 = (25t + 4.9t2) Solving 28 = 25t + 4.9t2 Solving for variable 't'. Reorder the terms: 28 + -25t + -4.9t2 = 25t + -25t + 4.9t2 + -4.9t2 Combine like terms: 25t + -25t = 0 28 + -25t + -4.9t2 = 0 + 4.9t2 + -4.9t2 28 + -25t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 28 + -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'. -5.714285714 + 5.102040816t + t2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + 5.102040816t + 5.714285714 + t2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + 5.102040816t + t2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + 5.102040816t + t2 = 0 + 5.714285714 5.102040816t + t2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 5.102040816t + t2 = 5.714285714 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 = 5.714285714 + 6.507705122 Reorder the terms: 6.507705122 + 5.102040816t + t2 = 5.714285714 + 6.507705122 Combine like terms: 5.714285714 + 6.507705122 = 12.221990836 6.507705122 + 5.102040816t + t2 = 12.221990836 Factor a perfect square on the left side: (t + 2.551020408)(t + 2.551020408) = 12.221990836 Calculate the square root of the right side: 3.495996401 Break this problem into two subproblems by setting (t + 2.551020408) equal to 3.495996401 and -3.495996401.Subproblem 1
t + 2.551020408 = 3.495996401 Simplifying t + 2.551020408 = 3.495996401 Reorder the terms: 2.551020408 + t = 3.495996401 Solving 2.551020408 + t = 3.495996401 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 = 3.495996401 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = 3.495996401 + -2.551020408 t = 3.495996401 + -2.551020408 Combine like terms: 3.495996401 + -2.551020408 = 0.944975993 t = 0.944975993 Simplifying t = 0.944975993Subproblem 2
t + 2.551020408 = -3.495996401 Simplifying t + 2.551020408 = -3.495996401 Reorder the terms: 2.551020408 + t = -3.495996401 Solving 2.551020408 + t = -3.495996401 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 = -3.495996401 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + t = -3.495996401 + -2.551020408 t = -3.495996401 + -2.551020408 Combine like terms: -3.495996401 + -2.551020408 = -6.047016809 t = -6.047016809 Simplifying t = -6.047016809Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.944975993, -6.047016809}
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