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Simplifying 25 = t(-4.9t + 25) Reorder the terms: 25 = t(25 + -4.9t) 25 = (25 * t + -4.9t * t) 25 = (25t + -4.9t2) Solving 25 = 25t + -4.9t2 Solving for variable 't'. Reorder the terms: 25 + -25t + 4.9t2 = 25t + -25t + -4.9t2 + 4.9t2 Combine like terms: 25t + -25t = 0 25 + -25t + 4.9t2 = 0 + -4.9t2 + 4.9t2 25 + -25t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 25 + -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'. 5.102040816 + -5.102040816t + t2 = 0 Move the constant term to the right: Add '-5.102040816' to each side of the equation. 5.102040816 + -5.102040816t + -5.102040816 + t2 = 0 + -5.102040816 Reorder the terms: 5.102040816 + -5.102040816 + -5.102040816t + t2 = 0 + -5.102040816 Combine like terms: 5.102040816 + -5.102040816 = 0.000000000 0.000000000 + -5.102040816t + t2 = 0 + -5.102040816 -5.102040816t + t2 = 0 + -5.102040816 Combine like terms: 0 + -5.102040816 = -5.102040816 -5.102040816t + t2 = -5.102040816 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 = -5.102040816 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816t + t2 = -5.102040816 + 6.507705122 Combine like terms: -5.102040816 + 6.507705122 = 1.405664306 6.507705122 + -5.102040816t + t2 = 1.405664306 Factor a perfect square on the left side: (t + -2.551020408)(t + -2.551020408) = 1.405664306 Calculate the square root of the right side: 1.185607147 Break this problem into two subproblems by setting (t + -2.551020408) equal to 1.185607147 and -1.185607147.Subproblem 1
t + -2.551020408 = 1.185607147 Simplifying t + -2.551020408 = 1.185607147 Reorder the terms: -2.551020408 + t = 1.185607147 Solving -2.551020408 + t = 1.185607147 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 = 1.185607147 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = 1.185607147 + 2.551020408 t = 1.185607147 + 2.551020408 Combine like terms: 1.185607147 + 2.551020408 = 3.736627555 t = 3.736627555 Simplifying t = 3.736627555Subproblem 2
t + -2.551020408 = -1.185607147 Simplifying t + -2.551020408 = -1.185607147 Reorder the terms: -2.551020408 + t = -1.185607147 Solving -2.551020408 + t = -1.185607147 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 = -1.185607147 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = -1.185607147 + 2.551020408 t = -1.185607147 + 2.551020408 Combine like terms: -1.185607147 + 2.551020408 = 1.365413261 t = 1.365413261 Simplifying t = 1.365413261Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.736627555, 1.365413261}
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