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Simplifying 0 = -4.9t2 + 10t + 11 Reorder the terms: 0 = 11 + 10t + -4.9t2 Solving 0 = 11 + 10t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -11 = -11 -11 + -10t + 4.9t2 = 11 + 10t + -4.9t2 + -11 + -10t + 4.9t2 Reorder the terms: -11 + -10t + 4.9t2 = 11 + -11 + 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: 11 + -11 = 0 -11 + -10t + 4.9t2 = 0 + 10t + -10t + -4.9t2 + 4.9t2 -11 + -10t + 4.9t2 = 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: 10t + -10t = 0 -11 + -10t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -11 + -10t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -11 + -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'. -2.244897959 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '2.244897959' to each side of the equation. -2.244897959 + -2.040816327t + 2.244897959 + t2 = 0 + 2.244897959 Reorder the terms: -2.244897959 + 2.244897959 + -2.040816327t + t2 = 0 + 2.244897959 Combine like terms: -2.244897959 + 2.244897959 = 0.000000000 0.000000000 + -2.040816327t + t2 = 0 + 2.244897959 -2.040816327t + t2 = 0 + 2.244897959 Combine like terms: 0 + 2.244897959 = 2.244897959 -2.040816327t + t2 = 2.244897959 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 = 2.244897959 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 2.244897959 + 1.041232821 Combine like terms: 2.244897959 + 1.041232821 = 3.28613078 1.041232821 + -2.040816327t + t2 = 3.28613078 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 3.28613078 Calculate the square root of the right side: 1.812768816 Break this problem into two subproblems by setting (t + -1.020408164) equal to 1.812768816 and -1.812768816.Subproblem 1
t + -1.020408164 = 1.812768816 Simplifying t + -1.020408164 = 1.812768816 Reorder the terms: -1.020408164 + t = 1.812768816 Solving -1.020408164 + t = 1.812768816 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 = 1.812768816 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 1.812768816 + 1.020408164 t = 1.812768816 + 1.020408164 Combine like terms: 1.812768816 + 1.020408164 = 2.83317698 t = 2.83317698 Simplifying t = 2.83317698Subproblem 2
t + -1.020408164 = -1.812768816 Simplifying t + -1.020408164 = -1.812768816 Reorder the terms: -1.020408164 + t = -1.812768816 Solving -1.020408164 + t = -1.812768816 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 = -1.812768816 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -1.812768816 + 1.020408164 t = -1.812768816 + 1.020408164 Combine like terms: -1.812768816 + 1.020408164 = -0.792360652 t = -0.792360652 Simplifying t = -0.792360652Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.83317698, -0.792360652}
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