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Simplifying 0 = -4.9t2 + 10t + 700 Reorder the terms: 0 = 700 + 10t + -4.9t2 Solving 0 = 700 + 10t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -700 = -700 -700 + -10t + 4.9t2 = 700 + 10t + -4.9t2 + -700 + -10t + 4.9t2 Reorder the terms: -700 + -10t + 4.9t2 = 700 + -700 + 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: 700 + -700 = 0 -700 + -10t + 4.9t2 = 0 + 10t + -10t + -4.9t2 + 4.9t2 -700 + -10t + 4.9t2 = 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: 10t + -10t = 0 -700 + -10t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -700 + -10t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -700 + -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'. -142.8571429 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '142.8571429' to each side of the equation. -142.8571429 + -2.040816327t + 142.8571429 + t2 = 0 + 142.8571429 Reorder the terms: -142.8571429 + 142.8571429 + -2.040816327t + t2 = 0 + 142.8571429 Combine like terms: -142.8571429 + 142.8571429 = 0.0000000 0.0000000 + -2.040816327t + t2 = 0 + 142.8571429 -2.040816327t + t2 = 0 + 142.8571429 Combine like terms: 0 + 142.8571429 = 142.8571429 -2.040816327t + t2 = 142.8571429 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 = 142.8571429 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 142.8571429 + 1.041232821 Combine like terms: 142.8571429 + 1.041232821 = 143.898375721 1.041232821 + -2.040816327t + t2 = 143.898375721 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 143.898375721 Calculate the square root of the right side: 11.995764908 Break this problem into two subproblems by setting (t + -1.020408164) equal to 11.995764908 and -11.995764908.Subproblem 1
t + -1.020408164 = 11.995764908 Simplifying t + -1.020408164 = 11.995764908 Reorder the terms: -1.020408164 + t = 11.995764908 Solving -1.020408164 + t = 11.995764908 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 = 11.995764908 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 11.995764908 + 1.020408164 t = 11.995764908 + 1.020408164 Combine like terms: 11.995764908 + 1.020408164 = 13.016173072 t = 13.016173072 Simplifying t = 13.016173072Subproblem 2
t + -1.020408164 = -11.995764908 Simplifying t + -1.020408164 = -11.995764908 Reorder the terms: -1.020408164 + t = -11.995764908 Solving -1.020408164 + t = -11.995764908 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 = -11.995764908 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -11.995764908 + 1.020408164 t = -11.995764908 + 1.020408164 Combine like terms: -11.995764908 + 1.020408164 = -10.975356744 t = -10.975356744 Simplifying t = -10.975356744Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.016173072, -10.975356744}
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