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Simplifying 200 = 4.9t2 + 20t Reorder the terms: 200 = 20t + 4.9t2 Solving 200 = 20t + 4.9t2 Solving for variable 't'. Reorder the terms: 200 + -20t + -4.9t2 = 20t + -20t + 4.9t2 + -4.9t2 Combine like terms: 20t + -20t = 0 200 + -20t + -4.9t2 = 0 + 4.9t2 + -4.9t2 200 + -20t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 200 + -20t + -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'. -40.81632653 + 4.081632653t + t2 = 0 Move the constant term to the right: Add '40.81632653' to each side of the equation. -40.81632653 + 4.081632653t + 40.81632653 + t2 = 0 + 40.81632653 Reorder the terms: -40.81632653 + 40.81632653 + 4.081632653t + t2 = 0 + 40.81632653 Combine like terms: -40.81632653 + 40.81632653 = 0.00000000 0.00000000 + 4.081632653t + t2 = 0 + 40.81632653 4.081632653t + t2 = 0 + 40.81632653 Combine like terms: 0 + 40.81632653 = 40.81632653 4.081632653t + t2 = 40.81632653 The t term is 4.081632653t. Take half its coefficient (2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. 4.081632653t + 4.164931281 + t2 = 40.81632653 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653t + t2 = 40.81632653 + 4.164931281 Combine like terms: 40.81632653 + 4.164931281 = 44.981257811 4.164931281 + 4.081632653t + t2 = 44.981257811 Factor a perfect square on the left side: (t + 2.040816327)(t + 2.040816327) = 44.981257811 Calculate the square root of the right side: 6.706806827 Break this problem into two subproblems by setting (t + 2.040816327) equal to 6.706806827 and -6.706806827.Subproblem 1
t + 2.040816327 = 6.706806827 Simplifying t + 2.040816327 = 6.706806827 Reorder the terms: 2.040816327 + t = 6.706806827 Solving 2.040816327 + t = 6.706806827 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + t = 6.706806827 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = 6.706806827 + -2.040816327 t = 6.706806827 + -2.040816327 Combine like terms: 6.706806827 + -2.040816327 = 4.6659905 t = 4.6659905 Simplifying t = 4.6659905Subproblem 2
t + 2.040816327 = -6.706806827 Simplifying t + 2.040816327 = -6.706806827 Reorder the terms: 2.040816327 + t = -6.706806827 Solving 2.040816327 + t = -6.706806827 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + t = -6.706806827 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = -6.706806827 + -2.040816327 t = -6.706806827 + -2.040816327 Combine like terms: -6.706806827 + -2.040816327 = -8.747623154 t = -8.747623154 Simplifying t = -8.747623154Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.6659905, -8.747623154}
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