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Simplifying 0 = -4.9t2 + 3.9t + 1 Reorder the terms: 0 = 1 + 3.9t + -4.9t2 Solving 0 = 1 + 3.9t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -1 = -1 -1 + -3.9t + 4.9t2 = 1 + 3.9t + -4.9t2 + -1 + -3.9t + 4.9t2 Reorder the terms: -1 + -3.9t + 4.9t2 = 1 + -1 + 3.9t + -3.9t + -4.9t2 + 4.9t2 Combine like terms: 1 + -1 = 0 -1 + -3.9t + 4.9t2 = 0 + 3.9t + -3.9t + -4.9t2 + 4.9t2 -1 + -3.9t + 4.9t2 = 3.9t + -3.9t + -4.9t2 + 4.9t2 Combine like terms: 3.9t + -3.9t = 0.0 -1 + -3.9t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -1 + -3.9t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -1 + -3.9t + 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'. -0.2040816327 + -0.7959183673t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -0.7959183673t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -0.7959183673t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -0.7959183673t + t2 = 0 + 0.2040816327 -0.7959183673t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -0.7959183673t + t2 = 0.2040816327 The t term is -0.7959183673t. Take half its coefficient (-0.3979591837). Square it (0.1583715119) and add it to both sides. Add '0.1583715119' to each side of the equation. -0.7959183673t + 0.1583715119 + t2 = 0.2040816327 + 0.1583715119 Reorder the terms: 0.1583715119 + -0.7959183673t + t2 = 0.2040816327 + 0.1583715119 Combine like terms: 0.2040816327 + 0.1583715119 = 0.3624531446 0.1583715119 + -0.7959183673t + t2 = 0.3624531446 Factor a perfect square on the left side: (t + -0.3979591837)(t + -0.3979591837) = 0.3624531446 Calculate the square root of the right side: 0.602040816 Break this problem into two subproblems by setting (t + -0.3979591837) equal to 0.602040816 and -0.602040816.Subproblem 1
t + -0.3979591837 = 0.602040816 Simplifying t + -0.3979591837 = 0.602040816 Reorder the terms: -0.3979591837 + t = 0.602040816 Solving -0.3979591837 + t = 0.602040816 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3979591837' to each side of the equation. -0.3979591837 + 0.3979591837 + t = 0.602040816 + 0.3979591837 Combine like terms: -0.3979591837 + 0.3979591837 = 0.0000000000 0.0000000000 + t = 0.602040816 + 0.3979591837 t = 0.602040816 + 0.3979591837 Combine like terms: 0.602040816 + 0.3979591837 = 0.9999999997 t = 0.9999999997 Simplifying t = 0.9999999997Subproblem 2
t + -0.3979591837 = -0.602040816 Simplifying t + -0.3979591837 = -0.602040816 Reorder the terms: -0.3979591837 + t = -0.602040816 Solving -0.3979591837 + t = -0.602040816 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3979591837' to each side of the equation. -0.3979591837 + 0.3979591837 + t = -0.602040816 + 0.3979591837 Combine like terms: -0.3979591837 + 0.3979591837 = 0.0000000000 0.0000000000 + t = -0.602040816 + 0.3979591837 t = -0.602040816 + 0.3979591837 Combine like terms: -0.602040816 + 0.3979591837 = -0.2040816323 t = -0.2040816323 Simplifying t = -0.2040816323Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.9999999997, -0.2040816323}
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