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Simplifying -10 = -4.9t2 + 20t Reorder the terms: -10 = 20t + -4.9t2 Solving -10 = 20t + -4.9t2 Solving for variable 't'. Reorder the terms: -10 + -20t + 4.9t2 = 20t + -20t + -4.9t2 + 4.9t2 Combine like terms: 20t + -20t = 0 -10 + -20t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -10 + -20t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -10 + -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'. -2.040816327 + -4.081632653t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -4.081632653t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -4.081632653t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -4.081632653t + t2 = 0 + 2.040816327 -4.081632653t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -4.081632653t + t2 = 2.040816327 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 = 2.040816327 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653t + t2 = 2.040816327 + 4.164931281 Combine like terms: 2.040816327 + 4.164931281 = 6.205747608 4.164931281 + -4.081632653t + t2 = 6.205747608 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 6.205747608 Calculate the square root of the right side: 2.4911338 Break this problem into two subproblems by setting (t + -2.040816327) equal to 2.4911338 and -2.4911338.Subproblem 1
t + -2.040816327 = 2.4911338 Simplifying t + -2.040816327 = 2.4911338 Reorder the terms: -2.040816327 + t = 2.4911338 Solving -2.040816327 + t = 2.4911338 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 = 2.4911338 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 2.4911338 + 2.040816327 t = 2.4911338 + 2.040816327 Combine like terms: 2.4911338 + 2.040816327 = 4.531950127 t = 4.531950127 Simplifying t = 4.531950127Subproblem 2
t + -2.040816327 = -2.4911338 Simplifying t + -2.040816327 = -2.4911338 Reorder the terms: -2.040816327 + t = -2.4911338 Solving -2.040816327 + t = -2.4911338 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 = -2.4911338 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -2.4911338 + 2.040816327 t = -2.4911338 + 2.040816327 Combine like terms: -2.4911338 + 2.040816327 = -0.450317473 t = -0.450317473 Simplifying t = -0.450317473Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.531950127, -0.450317473}
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