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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 = 4.3690129137 4.164931281 + -4.081632653t + t2 = 4.3690129137 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 4.3690129137 Calculate the square root of the right side: 2.090218389 Break this problem into two subproblems by setting (t + -2.040816327) equal to 2.090218389 and -2.090218389.Subproblem 1
t + -2.040816327 = 2.090218389 Simplifying t + -2.040816327 = 2.090218389 Reorder the terms: -2.040816327 + t = 2.090218389 Solving -2.040816327 + t = 2.090218389 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 = 2.090218389 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 2.090218389 + 2.040816327 t = 2.090218389 + 2.040816327 Combine like terms: 2.090218389 + 2.040816327 = 4.131034716 t = 4.131034716 Simplifying t = 4.131034716Subproblem 2
t + -2.040816327 = -2.090218389 Simplifying t + -2.040816327 = -2.090218389 Reorder the terms: -2.040816327 + t = -2.090218389 Solving -2.040816327 + t = -2.090218389 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 = -2.090218389 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -2.090218389 + 2.040816327 t = -2.090218389 + 2.040816327 Combine like terms: -2.090218389 + 2.040816327 = -0.049402062 t = -0.049402062 Simplifying t = -0.049402062Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.131034716, -0.049402062}
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