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Simplifying 0 = -4.9t2 + -10t + 120 Reorder the terms: 0 = 120 + -10t + -4.9t2 Solving 0 = 120 + -10t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -120 = -120 -120 + 10t + 4.9t2 = 120 + -10t + -4.9t2 + -120 + 10t + 4.9t2 Reorder the terms: -120 + 10t + 4.9t2 = 120 + -120 + -10t + 10t + -4.9t2 + 4.9t2 Combine like terms: 120 + -120 = 0 -120 + 10t + 4.9t2 = 0 + -10t + 10t + -4.9t2 + 4.9t2 -120 + 10t + 4.9t2 = -10t + 10t + -4.9t2 + 4.9t2 Combine like terms: -10t + 10t = 0 -120 + 10t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -120 + 10t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -120 + 10t + 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'. -24.48979592 + 2.040816327t + t2 = 0 Move the constant term to the right: Add '24.48979592' to each side of the equation. -24.48979592 + 2.040816327t + 24.48979592 + t2 = 0 + 24.48979592 Reorder the terms: -24.48979592 + 24.48979592 + 2.040816327t + t2 = 0 + 24.48979592 Combine like terms: -24.48979592 + 24.48979592 = 0.00000000 0.00000000 + 2.040816327t + t2 = 0 + 24.48979592 2.040816327t + t2 = 0 + 24.48979592 Combine like terms: 0 + 24.48979592 = 24.48979592 2.040816327t + t2 = 24.48979592 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 = 24.48979592 + 1.041232821 Reorder the terms: 1.041232821 + 2.040816327t + t2 = 24.48979592 + 1.041232821 Combine like terms: 24.48979592 + 1.041232821 = 25.531028741 1.041232821 + 2.040816327t + t2 = 25.531028741 Factor a perfect square on the left side: (t + 1.020408164)(t + 1.020408164) = 25.531028741 Calculate the square root of the right side: 5.052823838 Break this problem into two subproblems by setting (t + 1.020408164) equal to 5.052823838 and -5.052823838.Subproblem 1
t + 1.020408164 = 5.052823838 Simplifying t + 1.020408164 = 5.052823838 Reorder the terms: 1.020408164 + t = 5.052823838 Solving 1.020408164 + t = 5.052823838 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 = 5.052823838 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + t = 5.052823838 + -1.020408164 t = 5.052823838 + -1.020408164 Combine like terms: 5.052823838 + -1.020408164 = 4.032415674 t = 4.032415674 Simplifying t = 4.032415674Subproblem 2
t + 1.020408164 = -5.052823838 Simplifying t + 1.020408164 = -5.052823838 Reorder the terms: 1.020408164 + t = -5.052823838 Solving 1.020408164 + t = -5.052823838 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 = -5.052823838 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + t = -5.052823838 + -1.020408164 t = -5.052823838 + -1.020408164 Combine like terms: -5.052823838 + -1.020408164 = -6.073232002 t = -6.073232002 Simplifying t = -6.073232002Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.032415674, -6.073232002}
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