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Simplifying 0 = 38 + 25t + -4.9t2 Solving 0 = 38 + 25t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -38 = -38 -38 + -25t + 4.9t2 = 38 + 25t + -4.9t2 + -38 + -25t + 4.9t2 Reorder the terms: -38 + -25t + 4.9t2 = 38 + -38 + 25t + -25t + -4.9t2 + 4.9t2 Combine like terms: 38 + -38 = 0 -38 + -25t + 4.9t2 = 0 + 25t + -25t + -4.9t2 + 4.9t2 -38 + -25t + 4.9t2 = 25t + -25t + -4.9t2 + 4.9t2 Combine like terms: 25t + -25t = 0 -38 + -25t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -38 + -25t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -38 + -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'. -7.755102041 + -5.102040816t + t2 = 0 Move the constant term to the right: Add '7.755102041' to each side of the equation. -7.755102041 + -5.102040816t + 7.755102041 + t2 = 0 + 7.755102041 Reorder the terms: -7.755102041 + 7.755102041 + -5.102040816t + t2 = 0 + 7.755102041 Combine like terms: -7.755102041 + 7.755102041 = 0.000000000 0.000000000 + -5.102040816t + t2 = 0 + 7.755102041 -5.102040816t + t2 = 0 + 7.755102041 Combine like terms: 0 + 7.755102041 = 7.755102041 -5.102040816t + t2 = 7.755102041 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 = 7.755102041 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816t + t2 = 7.755102041 + 6.507705122 Combine like terms: 7.755102041 + 6.507705122 = 14.262807163 6.507705122 + -5.102040816t + t2 = 14.262807163 Factor a perfect square on the left side: (t + -2.551020408)(t + -2.551020408) = 14.262807163 Calculate the square root of the right side: 3.776613187 Break this problem into two subproblems by setting (t + -2.551020408) equal to 3.776613187 and -3.776613187.Subproblem 1
t + -2.551020408 = 3.776613187 Simplifying t + -2.551020408 = 3.776613187 Reorder the terms: -2.551020408 + t = 3.776613187 Solving -2.551020408 + t = 3.776613187 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 = 3.776613187 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = 3.776613187 + 2.551020408 t = 3.776613187 + 2.551020408 Combine like terms: 3.776613187 + 2.551020408 = 6.327633595 t = 6.327633595 Simplifying t = 6.327633595Subproblem 2
t + -2.551020408 = -3.776613187 Simplifying t + -2.551020408 = -3.776613187 Reorder the terms: -2.551020408 + t = -3.776613187 Solving -2.551020408 + t = -3.776613187 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 = -3.776613187 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + t = -3.776613187 + 2.551020408 t = -3.776613187 + 2.551020408 Combine like terms: -3.776613187 + 2.551020408 = -1.225592779 t = -1.225592779 Simplifying t = -1.225592779Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.327633595, -1.225592779}
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