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Simplifying 0 = -4.9t2 + 10t + 184 Reorder the terms: 0 = 184 + 10t + -4.9t2 Solving 0 = 184 + 10t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -184 = -184 -184 + -10t + 4.9t2 = 184 + 10t + -4.9t2 + -184 + -10t + 4.9t2 Reorder the terms: -184 + -10t + 4.9t2 = 184 + -184 + 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: 184 + -184 = 0 -184 + -10t + 4.9t2 = 0 + 10t + -10t + -4.9t2 + 4.9t2 -184 + -10t + 4.9t2 = 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: 10t + -10t = 0 -184 + -10t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -184 + -10t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -184 + -10t + 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'. -37.55102041 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '37.55102041' to each side of the equation. -37.55102041 + -2.040816327t + 37.55102041 + t2 = 0 + 37.55102041 Reorder the terms: -37.55102041 + 37.55102041 + -2.040816327t + t2 = 0 + 37.55102041 Combine like terms: -37.55102041 + 37.55102041 = 0.00000000 0.00000000 + -2.040816327t + t2 = 0 + 37.55102041 -2.040816327t + t2 = 0 + 37.55102041 Combine like terms: 0 + 37.55102041 = 37.55102041 -2.040816327t + t2 = 37.55102041 The t term is -2.040816327t. Take half its coefficient (-1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. -2.040816327t + 1.041232821 + t2 = 37.55102041 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 37.55102041 + 1.041232821 Combine like terms: 37.55102041 + 1.041232821 = 38.592253231 1.041232821 + -2.040816327t + t2 = 38.592253231 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 38.592253231 Calculate the square root of the right side: 6.212266352 Break this problem into two subproblems by setting (t + -1.020408164) equal to 6.212266352 and -6.212266352.Subproblem 1
t + -1.020408164 = 6.212266352 Simplifying t + -1.020408164 = 6.212266352 Reorder the terms: -1.020408164 + t = 6.212266352 Solving -1.020408164 + t = 6.212266352 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = 6.212266352 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 6.212266352 + 1.020408164 t = 6.212266352 + 1.020408164 Combine like terms: 6.212266352 + 1.020408164 = 7.232674516 t = 7.232674516 Simplifying t = 7.232674516Subproblem 2
t + -1.020408164 = -6.212266352 Simplifying t + -1.020408164 = -6.212266352 Reorder the terms: -1.020408164 + t = -6.212266352 Solving -1.020408164 + t = -6.212266352 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = -6.212266352 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -6.212266352 + 1.020408164 t = -6.212266352 + 1.020408164 Combine like terms: -6.212266352 + 1.020408164 = -5.191858188 t = -5.191858188 Simplifying t = -5.191858188Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.232674516, -5.191858188}
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