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Simplifying 0 = -4.9t2 + 10t + -2 Reorder the terms: 0 = -2 + 10t + -4.9t2 Solving 0 = -2 + 10t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + 2 = 2 2 + -10t + 4.9t2 = -2 + 10t + -4.9t2 + 2 + -10t + 4.9t2 Reorder the terms: 2 + -10t + 4.9t2 = -2 + 2 + 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: -2 + 2 = 0 2 + -10t + 4.9t2 = 0 + 10t + -10t + -4.9t2 + 4.9t2 2 + -10t + 4.9t2 = 10t + -10t + -4.9t2 + 4.9t2 Combine like terms: 10t + -10t = 0 2 + -10t + 4.9t2 = 0 + -4.9t2 + 4.9t2 2 + -10t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 2 + -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'. 0.4081632653 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + -2.040816327t + -0.4081632653 + t2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + -2.040816327t + t2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + -2.040816327t + t2 = 0 + -0.4081632653 -2.040816327t + t2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 -2.040816327t + t2 = -0.4081632653 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 = -0.4081632653 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = -0.4081632653 + 1.041232821 Combine like terms: -0.4081632653 + 1.041232821 = 0.6330695557 1.041232821 + -2.040816327t + t2 = 0.6330695557 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 0.6330695557 Calculate the square root of the right side: 0.795656682 Break this problem into two subproblems by setting (t + -1.020408164) equal to 0.795656682 and -0.795656682.Subproblem 1
t + -1.020408164 = 0.795656682 Simplifying t + -1.020408164 = 0.795656682 Reorder the terms: -1.020408164 + t = 0.795656682 Solving -1.020408164 + t = 0.795656682 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 = 0.795656682 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 0.795656682 + 1.020408164 t = 0.795656682 + 1.020408164 Combine like terms: 0.795656682 + 1.020408164 = 1.816064846 t = 1.816064846 Simplifying t = 1.816064846Subproblem 2
t + -1.020408164 = -0.795656682 Simplifying t + -1.020408164 = -0.795656682 Reorder the terms: -1.020408164 + t = -0.795656682 Solving -1.020408164 + t = -0.795656682 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 = -0.795656682 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -0.795656682 + 1.020408164 t = -0.795656682 + 1.020408164 Combine like terms: -0.795656682 + 1.020408164 = 0.224751482 t = 0.224751482 Simplifying t = 0.224751482Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.816064846, 0.224751482}
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