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Simplifying 4.9t2 + -10t + -80 = 0 Reorder the terms: -80 + -10t + 4.9t2 = 0 Solving -80 + -10t + 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'. -16.32653061 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '16.32653061' to each side of the equation. -16.32653061 + -2.040816327t + 16.32653061 + t2 = 0 + 16.32653061 Reorder the terms: -16.32653061 + 16.32653061 + -2.040816327t + t2 = 0 + 16.32653061 Combine like terms: -16.32653061 + 16.32653061 = 0.00000000 0.00000000 + -2.040816327t + t2 = 0 + 16.32653061 -2.040816327t + t2 = 0 + 16.32653061 Combine like terms: 0 + 16.32653061 = 16.32653061 -2.040816327t + t2 = 16.32653061 The t term is -2.040816327t. Take half its coefficient (-1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. -2.040816327t + 1.041232821 + t2 = 16.32653061 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 16.32653061 + 1.041232821 Combine like terms: 16.32653061 + 1.041232821 = 17.367763431 1.041232821 + -2.040816327t + t2 = 17.367763431 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 17.367763431 Calculate the square root of the right side: 4.167464869 Break this problem into two subproblems by setting (t + -1.020408164) equal to 4.167464869 and -4.167464869.Subproblem 1
t + -1.020408164 = 4.167464869 Simplifying t + -1.020408164 = 4.167464869 Reorder the terms: -1.020408164 + t = 4.167464869 Solving -1.020408164 + t = 4.167464869 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = 4.167464869 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 4.167464869 + 1.020408164 t = 4.167464869 + 1.020408164 Combine like terms: 4.167464869 + 1.020408164 = 5.187873033 t = 5.187873033 Simplifying t = 5.187873033Subproblem 2
t + -1.020408164 = -4.167464869 Simplifying t + -1.020408164 = -4.167464869 Reorder the terms: -1.020408164 + t = -4.167464869 Solving -1.020408164 + t = -4.167464869 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = -4.167464869 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -4.167464869 + 1.020408164 t = -4.167464869 + 1.020408164 Combine like terms: -4.167464869 + 1.020408164 = -3.147056705 t = -3.147056705 Simplifying t = -3.147056705Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.187873033, -3.147056705}
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