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Simplifying 170 = -4.5t + 4.9t2 Solving 170 = -4.5t + 4.9t2 Solving for variable 't'. Reorder the terms: 170 + 4.5t + -4.9t2 = -4.5t + 4.5t + 4.9t2 + -4.9t2 Combine like terms: -4.5t + 4.5t = 0.0 170 + 4.5t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2 170 + 4.5t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 170 + 4.5t + -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'. -34.69387755 + -0.9183673469t + t2 = 0 Move the constant term to the right: Add '34.69387755' to each side of the equation. -34.69387755 + -0.9183673469t + 34.69387755 + t2 = 0 + 34.69387755 Reorder the terms: -34.69387755 + 34.69387755 + -0.9183673469t + t2 = 0 + 34.69387755 Combine like terms: -34.69387755 + 34.69387755 = 0.00000000 0.00000000 + -0.9183673469t + t2 = 0 + 34.69387755 -0.9183673469t + t2 = 0 + 34.69387755 Combine like terms: 0 + 34.69387755 = 34.69387755 -0.9183673469t + t2 = 34.69387755 The t term is -0.9183673469t. Take half its coefficient (-0.4591836735). Square it (0.2108496460) and add it to both sides. Add '0.2108496460' to each side of the equation. -0.9183673469t + 0.2108496460 + t2 = 34.69387755 + 0.2108496460 Reorder the terms: 0.2108496460 + -0.9183673469t + t2 = 34.69387755 + 0.2108496460 Combine like terms: 34.69387755 + 0.2108496460 = 34.904727196 0.2108496460 + -0.9183673469t + t2 = 34.904727196 Factor a perfect square on the left side: (t + -0.4591836735)(t + -0.4591836735) = 34.904727196 Calculate the square root of the right side: 5.908022275 Break this problem into two subproblems by setting (t + -0.4591836735) equal to 5.908022275 and -5.908022275.Subproblem 1
t + -0.4591836735 = 5.908022275 Simplifying t + -0.4591836735 = 5.908022275 Reorder the terms: -0.4591836735 + t = 5.908022275 Solving -0.4591836735 + t = 5.908022275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4591836735' to each side of the equation. -0.4591836735 + 0.4591836735 + t = 5.908022275 + 0.4591836735 Combine like terms: -0.4591836735 + 0.4591836735 = 0.0000000000 0.0000000000 + t = 5.908022275 + 0.4591836735 t = 5.908022275 + 0.4591836735 Combine like terms: 5.908022275 + 0.4591836735 = 6.3672059485 t = 6.3672059485 Simplifying t = 6.3672059485Subproblem 2
t + -0.4591836735 = -5.908022275 Simplifying t + -0.4591836735 = -5.908022275 Reorder the terms: -0.4591836735 + t = -5.908022275 Solving -0.4591836735 + t = -5.908022275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4591836735' to each side of the equation. -0.4591836735 + 0.4591836735 + t = -5.908022275 + 0.4591836735 Combine like terms: -0.4591836735 + 0.4591836735 = 0.0000000000 0.0000000000 + t = -5.908022275 + 0.4591836735 t = -5.908022275 + 0.4591836735 Combine like terms: -5.908022275 + 0.4591836735 = -5.4488386015 t = -5.4488386015 Simplifying t = -5.4488386015Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.3672059485, -5.4488386015}
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