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Simplifying 2.8 = -2.0t + 9.8t2 Solving 2.8 = -2.0t + 9.8t2 Solving for variable 't'. Reorder the terms: 2.8 + 2.0t + -9.8t2 = -2.0t + 2.0t + 9.8t2 + -9.8t2 Combine like terms: -2.0t + 2.0t = 0.0 2.8 + 2.0t + -9.8t2 = 0.0 + 9.8t2 + -9.8t2 2.8 + 2.0t + -9.8t2 = 9.8t2 + -9.8t2 Combine like terms: 9.8t2 + -9.8t2 = 0.0 2.8 + 2.0t + -9.8t2 = 0.0 Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -0.2857142857 + -0.2040816327t + t2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -0.2040816327t + 0.2857142857 + t2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -0.2040816327t + t2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -0.2040816327t + t2 = 0 + 0.2857142857 -0.2040816327t + t2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -0.2040816327t + t2 = 0.2857142857 The t term is -0.2040816327t. Take half its coefficient (-0.1020408164). Square it (0.01041232821) and add it to both sides. Add '0.01041232821' to each side of the equation. -0.2040816327t + 0.01041232821 + t2 = 0.2857142857 + 0.01041232821 Reorder the terms: 0.01041232821 + -0.2040816327t + t2 = 0.2857142857 + 0.01041232821 Combine like terms: 0.2857142857 + 0.01041232821 = 0.29612661391 0.01041232821 + -0.2040816327t + t2 = 0.29612661391 Factor a perfect square on the left side: (t + -0.1020408164)(t + -0.1020408164) = 0.29612661391 Calculate the square root of the right side: 0.544175168 Break this problem into two subproblems by setting (t + -0.1020408164) equal to 0.544175168 and -0.544175168.Subproblem 1
t + -0.1020408164 = 0.544175168 Simplifying t + -0.1020408164 = 0.544175168 Reorder the terms: -0.1020408164 + t = 0.544175168 Solving -0.1020408164 + t = 0.544175168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1020408164' to each side of the equation. -0.1020408164 + 0.1020408164 + t = 0.544175168 + 0.1020408164 Combine like terms: -0.1020408164 + 0.1020408164 = 0.0000000000 0.0000000000 + t = 0.544175168 + 0.1020408164 t = 0.544175168 + 0.1020408164 Combine like terms: 0.544175168 + 0.1020408164 = 0.6462159844 t = 0.6462159844 Simplifying t = 0.6462159844Subproblem 2
t + -0.1020408164 = -0.544175168 Simplifying t + -0.1020408164 = -0.544175168 Reorder the terms: -0.1020408164 + t = -0.544175168 Solving -0.1020408164 + t = -0.544175168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1020408164' to each side of the equation. -0.1020408164 + 0.1020408164 + t = -0.544175168 + 0.1020408164 Combine like terms: -0.1020408164 + 0.1020408164 = 0.0000000000 0.0000000000 + t = -0.544175168 + 0.1020408164 t = -0.544175168 + 0.1020408164 Combine like terms: -0.544175168 + 0.1020408164 = -0.4421343516 t = -0.4421343516 Simplifying t = -0.4421343516Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6462159844, -0.4421343516}
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