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Simplifying -4.9t2 + -20t + 80 = 0 Reorder the terms: 80 + -20t + -4.9t2 = 0 Solving 80 + -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'. -16.32653061 + 4.081632653t + t2 = 0 Move the constant term to the right: Add '16.32653061' to each side of the equation. -16.32653061 + 4.081632653t + 16.32653061 + t2 = 0 + 16.32653061 Reorder the terms: -16.32653061 + 16.32653061 + 4.081632653t + t2 = 0 + 16.32653061 Combine like terms: -16.32653061 + 16.32653061 = 0.00000000 0.00000000 + 4.081632653t + t2 = 0 + 16.32653061 4.081632653t + t2 = 0 + 16.32653061 Combine like terms: 0 + 16.32653061 = 16.32653061 4.081632653t + t2 = 16.32653061 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 = 16.32653061 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653t + t2 = 16.32653061 + 4.164931281 Combine like terms: 16.32653061 + 4.164931281 = 20.491461891 4.164931281 + 4.081632653t + t2 = 20.491461891 Factor a perfect square on the left side: (t + 2.040816327)(t + 2.040816327) = 20.491461891 Calculate the square root of the right side: 4.526749594 Break this problem into two subproblems by setting (t + 2.040816327) equal to 4.526749594 and -4.526749594.Subproblem 1
t + 2.040816327 = 4.526749594 Simplifying t + 2.040816327 = 4.526749594 Reorder the terms: 2.040816327 + t = 4.526749594 Solving 2.040816327 + t = 4.526749594 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 = 4.526749594 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = 4.526749594 + -2.040816327 t = 4.526749594 + -2.040816327 Combine like terms: 4.526749594 + -2.040816327 = 2.485933267 t = 2.485933267 Simplifying t = 2.485933267Subproblem 2
t + 2.040816327 = -4.526749594 Simplifying t + 2.040816327 = -4.526749594 Reorder the terms: 2.040816327 + t = -4.526749594 Solving 2.040816327 + t = -4.526749594 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 = -4.526749594 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = -4.526749594 + -2.040816327 t = -4.526749594 + -2.040816327 Combine like terms: -4.526749594 + -2.040816327 = -6.567565921 t = -6.567565921 Simplifying t = -6.567565921Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.485933267, -6.567565921}
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