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Simplifying -4.9t2 + 54t + 40 = 0 Reorder the terms: 40 + 54t + -4.9t2 = 0 Solving 40 + 54t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -8.163265306 + -11.02040816t + t2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + -11.02040816t + 8.163265306 + t2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + -11.02040816t + t2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + -11.02040816t + t2 = 0 + 8.163265306 -11.02040816t + t2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 -11.02040816t + t2 = 8.163265306 The t term is -11.02040816t. Take half its coefficient (-5.51020408). Square it (30.36234900) and add it to both sides. Add '30.36234900' to each side of the equation. -11.02040816t + 30.36234900 + t2 = 8.163265306 + 30.36234900 Reorder the terms: 30.36234900 + -11.02040816t + t2 = 8.163265306 + 30.36234900 Combine like terms: 8.163265306 + 30.36234900 = 38.525614306 30.36234900 + -11.02040816t + t2 = 38.525614306 Factor a perfect square on the left side: (t + -5.51020408)(t + -5.51020408) = 38.525614306 Calculate the square root of the right side: 6.206900539 Break this problem into two subproblems by setting (t + -5.51020408) equal to 6.206900539 and -6.206900539.Subproblem 1
t + -5.51020408 = 6.206900539 Simplifying t + -5.51020408 = 6.206900539 Reorder the terms: -5.51020408 + t = 6.206900539 Solving -5.51020408 + t = 6.206900539 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.51020408' to each side of the equation. -5.51020408 + 5.51020408 + t = 6.206900539 + 5.51020408 Combine like terms: -5.51020408 + 5.51020408 = 0.00000000 0.00000000 + t = 6.206900539 + 5.51020408 t = 6.206900539 + 5.51020408 Combine like terms: 6.206900539 + 5.51020408 = 11.717104619 t = 11.717104619 Simplifying t = 11.717104619Subproblem 2
t + -5.51020408 = -6.206900539 Simplifying t + -5.51020408 = -6.206900539 Reorder the terms: -5.51020408 + t = -6.206900539 Solving -5.51020408 + t = -6.206900539 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.51020408' to each side of the equation. -5.51020408 + 5.51020408 + t = -6.206900539 + 5.51020408 Combine like terms: -5.51020408 + 5.51020408 = 0.00000000 0.00000000 + t = -6.206900539 + 5.51020408 t = -6.206900539 + 5.51020408 Combine like terms: -6.206900539 + 5.51020408 = -0.696696459 t = -0.696696459 Simplifying t = -0.696696459Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.717104619, -0.696696459}
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