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Simplifying 86 = -10t + 4.9t2 Solving 86 = -10t + 4.9t2 Solving for variable 't'. Reorder the terms: 86 + 10t + -4.9t2 = -10t + 10t + 4.9t2 + -4.9t2 Combine like terms: -10t + 10t = 0 86 + 10t + -4.9t2 = 0 + 4.9t2 + -4.9t2 86 + 10t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 86 + 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'. -17.55102041 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '17.55102041' to each side of the equation. -17.55102041 + -2.040816327t + 17.55102041 + t2 = 0 + 17.55102041 Reorder the terms: -17.55102041 + 17.55102041 + -2.040816327t + t2 = 0 + 17.55102041 Combine like terms: -17.55102041 + 17.55102041 = 0.00000000 0.00000000 + -2.040816327t + t2 = 0 + 17.55102041 -2.040816327t + t2 = 0 + 17.55102041 Combine like terms: 0 + 17.55102041 = 17.55102041 -2.040816327t + t2 = 17.55102041 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 = 17.55102041 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 17.55102041 + 1.041232821 Combine like terms: 17.55102041 + 1.041232821 = 18.592253231 1.041232821 + -2.040816327t + t2 = 18.592253231 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 18.592253231 Calculate the square root of the right side: 4.311873518 Break this problem into two subproblems by setting (t + -1.020408164) equal to 4.311873518 and -4.311873518.Subproblem 1
t + -1.020408164 = 4.311873518 Simplifying t + -1.020408164 = 4.311873518 Reorder the terms: -1.020408164 + t = 4.311873518 Solving -1.020408164 + t = 4.311873518 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 = 4.311873518 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 4.311873518 + 1.020408164 t = 4.311873518 + 1.020408164 Combine like terms: 4.311873518 + 1.020408164 = 5.332281682 t = 5.332281682 Simplifying t = 5.332281682Subproblem 2
t + -1.020408164 = -4.311873518 Simplifying t + -1.020408164 = -4.311873518 Reorder the terms: -1.020408164 + t = -4.311873518 Solving -1.020408164 + t = -4.311873518 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 = -4.311873518 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -4.311873518 + 1.020408164 t = -4.311873518 + 1.020408164 Combine like terms: -4.311873518 + 1.020408164 = -3.291465354 t = -3.291465354 Simplifying t = -3.291465354Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.332281682, -3.291465354}
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