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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 = 22.199083694 30.36234900 + -11.02040816t + t2 = 22.199083694 Factor a perfect square on the left side: (t + -5.51020408)(t + -5.51020408) = 22.199083694 Calculate the square root of the right side: 4.711590357 Break this problem into two subproblems by setting (t + -5.51020408) equal to 4.711590357 and -4.711590357.Subproblem 1
t + -5.51020408 = 4.711590357 Simplifying t + -5.51020408 = 4.711590357 Reorder the terms: -5.51020408 + t = 4.711590357 Solving -5.51020408 + t = 4.711590357 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 = 4.711590357 + 5.51020408 Combine like terms: -5.51020408 + 5.51020408 = 0.00000000 0.00000000 + t = 4.711590357 + 5.51020408 t = 4.711590357 + 5.51020408 Combine like terms: 4.711590357 + 5.51020408 = 10.221794437 t = 10.221794437 Simplifying t = 10.221794437Subproblem 2
t + -5.51020408 = -4.711590357 Simplifying t + -5.51020408 = -4.711590357 Reorder the terms: -5.51020408 + t = -4.711590357 Solving -5.51020408 + t = -4.711590357 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 = -4.711590357 + 5.51020408 Combine like terms: -5.51020408 + 5.51020408 = 0.00000000 0.00000000 + t = -4.711590357 + 5.51020408 t = -4.711590357 + 5.51020408 Combine like terms: -4.711590357 + 5.51020408 = 0.798613723 t = 0.798613723 Simplifying t = 0.798613723Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.221794437, 0.798613723}
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