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Simplifying 86 = -9.8t + 5t2 Solving 86 = -9.8t + 5t2 Solving for variable 't'. Reorder the terms: 86 + 9.8t + -5t2 = -9.8t + 9.8t + 5t2 + -5t2 Combine like terms: -9.8t + 9.8t = 0.0 86 + 9.8t + -5t2 = 0.0 + 5t2 + -5t2 86 + 9.8t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 86 + 9.8t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -17.2 + -1.96t + t2 = 0 Move the constant term to the right: Add '17.2' to each side of the equation. -17.2 + -1.96t + 17.2 + t2 = 0 + 17.2 Reorder the terms: -17.2 + 17.2 + -1.96t + t2 = 0 + 17.2 Combine like terms: -17.2 + 17.2 = 0.0 0.0 + -1.96t + t2 = 0 + 17.2 -1.96t + t2 = 0 + 17.2 Combine like terms: 0 + 17.2 = 17.2 -1.96t + t2 = 17.2 The t term is -1.96t. Take half its coefficient (-0.98). Square it (0.9604) and add it to both sides. Add '0.9604' to each side of the equation. -1.96t + 0.9604 + t2 = 17.2 + 0.9604 Reorder the terms: 0.9604 + -1.96t + t2 = 17.2 + 0.9604 Combine like terms: 17.2 + 0.9604 = 18.1604 0.9604 + -1.96t + t2 = 18.1604 Factor a perfect square on the left side: (t + -0.98)(t + -0.98) = 18.1604 Calculate the square root of the right side: 4.261502083 Break this problem into two subproblems by setting (t + -0.98) equal to 4.261502083 and -4.261502083.Subproblem 1
t + -0.98 = 4.261502083 Simplifying t + -0.98 = 4.261502083 Reorder the terms: -0.98 + t = 4.261502083 Solving -0.98 + t = 4.261502083 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.98' to each side of the equation. -0.98 + 0.98 + t = 4.261502083 + 0.98 Combine like terms: -0.98 + 0.98 = 0.00 0.00 + t = 4.261502083 + 0.98 t = 4.261502083 + 0.98 Combine like terms: 4.261502083 + 0.98 = 5.241502083 t = 5.241502083 Simplifying t = 5.241502083Subproblem 2
t + -0.98 = -4.261502083 Simplifying t + -0.98 = -4.261502083 Reorder the terms: -0.98 + t = -4.261502083 Solving -0.98 + t = -4.261502083 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.98' to each side of the equation. -0.98 + 0.98 + t = -4.261502083 + 0.98 Combine like terms: -0.98 + 0.98 = 0.00 0.00 + t = -4.261502083 + 0.98 t = -4.261502083 + 0.98 Combine like terms: -4.261502083 + 0.98 = -3.281502083 t = -3.281502083 Simplifying t = -3.281502083Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.241502083, -3.281502083}
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