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Simplifying 4.9t2 + 20t + 1 = 0 Reorder the terms: 1 + 20t + 4.9t2 = 0 Solving 1 + 20t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.2040816327 + 4.081632653t + t2 = 0 Move the constant term to the right: Add '-0.2040816327' to each side of the equation. 0.2040816327 + 4.081632653t + -0.2040816327 + t2 = 0 + -0.2040816327 Reorder the terms: 0.2040816327 + -0.2040816327 + 4.081632653t + t2 = 0 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + 4.081632653t + t2 = 0 + -0.2040816327 4.081632653t + t2 = 0 + -0.2040816327 Combine like terms: 0 + -0.2040816327 = -0.2040816327 4.081632653t + t2 = -0.2040816327 The t term is 4.081632653t. Take half its coefficient (2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. 4.081632653t + 4.164931281 + t2 = -0.2040816327 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653t + t2 = -0.2040816327 + 4.164931281 Combine like terms: -0.2040816327 + 4.164931281 = 3.9608496483 4.164931281 + 4.081632653t + t2 = 3.9608496483 Factor a perfect square on the left side: (t + 2.040816327)(t + 2.040816327) = 3.9608496483 Calculate the square root of the right side: 1.990188345 Break this problem into two subproblems by setting (t + 2.040816327) equal to 1.990188345 and -1.990188345.Subproblem 1
t + 2.040816327 = 1.990188345 Simplifying t + 2.040816327 = 1.990188345 Reorder the terms: 2.040816327 + t = 1.990188345 Solving 2.040816327 + t = 1.990188345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + t = 1.990188345 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = 1.990188345 + -2.040816327 t = 1.990188345 + -2.040816327 Combine like terms: 1.990188345 + -2.040816327 = -0.050627982 t = -0.050627982 Simplifying t = -0.050627982Subproblem 2
t + 2.040816327 = -1.990188345 Simplifying t + 2.040816327 = -1.990188345 Reorder the terms: 2.040816327 + t = -1.990188345 Solving 2.040816327 + t = -1.990188345 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + t = -1.990188345 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = -1.990188345 + -2.040816327 t = -1.990188345 + -2.040816327 Combine like terms: -1.990188345 + -2.040816327 = -4.031004672 t = -4.031004672 Simplifying t = -4.031004672Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.050627982, -4.031004672}
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