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Simplifying 0 = -4.9t2 + 10t + 0.5 Reorder the terms: 0 = 0.5 + 10t + -4.9t2 Solving 0 = 0.5 + 10t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -0.5 = -0.5 -0.5 + -10t + 4.9t2 = 0.5 + 10t + -4.9t2 + -0.5 + -10t + 4.9t2 Reorder the terms: -0.5 + -10t + 4.9t2 = 0.5 + -0.5 + 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + -10t + 4.9t2 = 0.0 + 10t + -10t + -4.9t2 + 4.9t2 -0.5 + -10t + 4.9t2 = 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: 10t + -10t = 0 -0.5 + -10t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -0.5 + -10t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -0.5 + -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'. -0.1020408163 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '0.1020408163' to each side of the equation. -0.1020408163 + -2.040816327t + 0.1020408163 + t2 = 0 + 0.1020408163 Reorder the terms: -0.1020408163 + 0.1020408163 + -2.040816327t + t2 = 0 + 0.1020408163 Combine like terms: -0.1020408163 + 0.1020408163 = 0.0000000000 0.0000000000 + -2.040816327t + t2 = 0 + 0.1020408163 -2.040816327t + t2 = 0 + 0.1020408163 Combine like terms: 0 + 0.1020408163 = 0.1020408163 -2.040816327t + t2 = 0.1020408163 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 = 0.1020408163 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 0.1020408163 + 1.041232821 Combine like terms: 0.1020408163 + 1.041232821 = 1.1432736373 1.041232821 + -2.040816327t + t2 = 1.1432736373 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 1.1432736373 Calculate the square root of the right side: 1.069239747 Break this problem into two subproblems by setting (t + -1.020408164) equal to 1.069239747 and -1.069239747.Subproblem 1
t + -1.020408164 = 1.069239747 Simplifying t + -1.020408164 = 1.069239747 Reorder the terms: -1.020408164 + t = 1.069239747 Solving -1.020408164 + t = 1.069239747 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 = 1.069239747 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 1.069239747 + 1.020408164 t = 1.069239747 + 1.020408164 Combine like terms: 1.069239747 + 1.020408164 = 2.089647911 t = 2.089647911 Simplifying t = 2.089647911Subproblem 2
t + -1.020408164 = -1.069239747 Simplifying t + -1.020408164 = -1.069239747 Reorder the terms: -1.020408164 + t = -1.069239747 Solving -1.020408164 + t = -1.069239747 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 = -1.069239747 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -1.069239747 + 1.020408164 t = -1.069239747 + 1.020408164 Combine like terms: -1.069239747 + 1.020408164 = -0.048831583 t = -0.048831583 Simplifying t = -0.048831583Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.089647911, -0.048831583}
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