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Simplifying 50 = 20t + 4.9t2 Solving 50 = 20t + 4.9t2 Solving for variable 't'. Reorder the terms: 50 + -20t + -4.9t2 = 20t + -20t + 4.9t2 + -4.9t2 Combine like terms: 20t + -20t = 0 50 + -20t + -4.9t2 = 0 + 4.9t2 + -4.9t2 50 + -20t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 50 + -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'. -10.20408163 + 4.081632653t + t2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 4.081632653t + 10.20408163 + t2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 4.081632653t + t2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 4.081632653t + t2 = 0 + 10.20408163 4.081632653t + t2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 4.081632653t + t2 = 10.20408163 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 = 10.20408163 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653t + t2 = 10.20408163 + 4.164931281 Combine like terms: 10.20408163 + 4.164931281 = 14.369012911 4.164931281 + 4.081632653t + t2 = 14.369012911 Factor a perfect square on the left side: (t + 2.040816327)(t + 2.040816327) = 14.369012911 Calculate the square root of the right side: 3.790648086 Break this problem into two subproblems by setting (t + 2.040816327) equal to 3.790648086 and -3.790648086.Subproblem 1
t + 2.040816327 = 3.790648086 Simplifying t + 2.040816327 = 3.790648086 Reorder the terms: 2.040816327 + t = 3.790648086 Solving 2.040816327 + t = 3.790648086 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 = 3.790648086 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = 3.790648086 + -2.040816327 t = 3.790648086 + -2.040816327 Combine like terms: 3.790648086 + -2.040816327 = 1.749831759 t = 1.749831759 Simplifying t = 1.749831759Subproblem 2
t + 2.040816327 = -3.790648086 Simplifying t + 2.040816327 = -3.790648086 Reorder the terms: 2.040816327 + t = -3.790648086 Solving 2.040816327 + t = -3.790648086 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 = -3.790648086 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + t = -3.790648086 + -2.040816327 t = -3.790648086 + -2.040816327 Combine like terms: -3.790648086 + -2.040816327 = -5.831464413 t = -5.831464413 Simplifying t = -5.831464413Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.749831759, -5.831464413}
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