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Simplifying -4.9t2 + 20t + 50 = 0 Reorder the terms: 50 + 20t + -4.9t2 = 0 Solving 50 + 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'. -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 = 5.831464413 t = 5.831464413 Simplifying t = 5.831464413Subproblem 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 = -1.749831759 t = -1.749831759 Simplifying t = -1.749831759Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.831464413, -1.749831759}
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