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Simplifying 13.877 = -4.9t2 + 68t Reorder the terms: 13.877 = 68t + -4.9t2 Solving 13.877 = 68t + -4.9t2 Solving for variable 't'. Reorder the terms: 13.877 + -68t + 4.9t2 = 68t + -68t + -4.9t2 + 4.9t2 Combine like terms: 68t + -68t = 0 13.877 + -68t + 4.9t2 = 0 + -4.9t2 + 4.9t2 13.877 + -68t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 13.877 + -68t + 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'. 2.832040816 + -13.87755102t + t2 = 0 Move the constant term to the right: Add '-2.832040816' to each side of the equation. 2.832040816 + -13.87755102t + -2.832040816 + t2 = 0 + -2.832040816 Reorder the terms: 2.832040816 + -2.832040816 + -13.87755102t + t2 = 0 + -2.832040816 Combine like terms: 2.832040816 + -2.832040816 = 0.000000000 0.000000000 + -13.87755102t + t2 = 0 + -2.832040816 -13.87755102t + t2 = 0 + -2.832040816 Combine like terms: 0 + -2.832040816 = -2.832040816 -13.87755102t + t2 = -2.832040816 The t term is -13.87755102t. Take half its coefficient (-6.93877551). Square it (48.14660558) and add it to both sides. Add '48.14660558' to each side of the equation. -13.87755102t + 48.14660558 + t2 = -2.832040816 + 48.14660558 Reorder the terms: 48.14660558 + -13.87755102t + t2 = -2.832040816 + 48.14660558 Combine like terms: -2.832040816 + 48.14660558 = 45.314564764 48.14660558 + -13.87755102t + t2 = 45.314564764 Factor a perfect square on the left side: (t + -6.93877551)(t + -6.93877551) = 45.314564764 Calculate the square root of the right side: 6.731609374 Break this problem into two subproblems by setting (t + -6.93877551) equal to 6.731609374 and -6.731609374.Subproblem 1
t + -6.93877551 = 6.731609374 Simplifying t + -6.93877551 = 6.731609374 Reorder the terms: -6.93877551 + t = 6.731609374 Solving -6.93877551 + t = 6.731609374 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.93877551' to each side of the equation. -6.93877551 + 6.93877551 + t = 6.731609374 + 6.93877551 Combine like terms: -6.93877551 + 6.93877551 = 0.00000000 0.00000000 + t = 6.731609374 + 6.93877551 t = 6.731609374 + 6.93877551 Combine like terms: 6.731609374 + 6.93877551 = 13.670384884 t = 13.670384884 Simplifying t = 13.670384884Subproblem 2
t + -6.93877551 = -6.731609374 Simplifying t + -6.93877551 = -6.731609374 Reorder the terms: -6.93877551 + t = -6.731609374 Solving -6.93877551 + t = -6.731609374 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.93877551' to each side of the equation. -6.93877551 + 6.93877551 + t = -6.731609374 + 6.93877551 Combine like terms: -6.93877551 + 6.93877551 = 0.00000000 0.00000000 + t = -6.731609374 + 6.93877551 t = -6.731609374 + 6.93877551 Combine like terms: -6.731609374 + 6.93877551 = 0.207166136 t = 0.207166136 Simplifying t = 0.207166136Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.670384884, 0.207166136}
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