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Simplifying 0 = -4.9t2 + 20t + -2 Reorder the terms: 0 = -2 + 20t + -4.9t2 Solving 0 = -2 + 20t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + 2 = 2 2 + -20t + 4.9t2 = -2 + 20t + -4.9t2 + 2 + -20t + 4.9t2 Reorder the terms: 2 + -20t + 4.9t2 = -2 + 2 + 20t + -20t + -4.9t2 + 4.9t2 Combine like terms: -2 + 2 = 0 2 + -20t + 4.9t2 = 0 + 20t + -20t + -4.9t2 + 4.9t2 2 + -20t + 4.9t2 = 20t + -20t + -4.9t2 + 4.9t2 Combine like terms: 20t + -20t = 0 2 + -20t + 4.9t2 = 0 + -4.9t2 + 4.9t2 2 + -20t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 2 + -20t + 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'. 0.4081632653 + -4.081632653t + t2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + -4.081632653t + -0.4081632653 + t2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + -4.081632653t + t2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + -4.081632653t + t2 = 0 + -0.4081632653 -4.081632653t + t2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 -4.081632653t + t2 = -0.4081632653 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 = -0.4081632653 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653t + t2 = -0.4081632653 + 4.164931281 Combine like terms: -0.4081632653 + 4.164931281 = 3.7567680157 4.164931281 + -4.081632653t + t2 = 3.7567680157 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 3.7567680157 Calculate the square root of the right side: 1.938238379 Break this problem into two subproblems by setting (t + -2.040816327) equal to 1.938238379 and -1.938238379.Subproblem 1
t + -2.040816327 = 1.938238379 Simplifying t + -2.040816327 = 1.938238379 Reorder the terms: -2.040816327 + t = 1.938238379 Solving -2.040816327 + t = 1.938238379 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 = 1.938238379 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 1.938238379 + 2.040816327 t = 1.938238379 + 2.040816327 Combine like terms: 1.938238379 + 2.040816327 = 3.979054706 t = 3.979054706 Simplifying t = 3.979054706Subproblem 2
t + -2.040816327 = -1.938238379 Simplifying t + -2.040816327 = -1.938238379 Reorder the terms: -2.040816327 + t = -1.938238379 Solving -2.040816327 + t = -1.938238379 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 = -1.938238379 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -1.938238379 + 2.040816327 t = -1.938238379 + 2.040816327 Combine like terms: -1.938238379 + 2.040816327 = 0.102577948 t = 0.102577948 Simplifying t = 0.102577948Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.979054706, 0.102577948}
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