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Simplifying 15 = -4.9t2 + 20t Reorder the terms: 15 = 20t + -4.9t2 Solving 15 = 20t + -4.9t2 Solving for variable 't'. Reorder the terms: 15 + -20t + 4.9t2 = 20t + -20t + -4.9t2 + 4.9t2 Combine like terms: 20t + -20t = 0 15 + -20t + 4.9t2 = 0 + -4.9t2 + 4.9t2 15 + -20t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 15 + -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'. 3.06122449 + -4.081632653t + t2 = 0 Move the constant term to the right: Add '-3.06122449' to each side of the equation. 3.06122449 + -4.081632653t + -3.06122449 + t2 = 0 + -3.06122449 Reorder the terms: 3.06122449 + -3.06122449 + -4.081632653t + t2 = 0 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + -4.081632653t + t2 = 0 + -3.06122449 -4.081632653t + t2 = 0 + -3.06122449 Combine like terms: 0 + -3.06122449 = -3.06122449 -4.081632653t + t2 = -3.06122449 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 = -3.06122449 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653t + t2 = -3.06122449 + 4.164931281 Combine like terms: -3.06122449 + 4.164931281 = 1.103706791 4.164931281 + -4.081632653t + t2 = 1.103706791 Factor a perfect square on the left side: (t + -2.040816327)(t + -2.040816327) = 1.103706791 Calculate the square root of the right side: 1.050574505 Break this problem into two subproblems by setting (t + -2.040816327) equal to 1.050574505 and -1.050574505.Subproblem 1
t + -2.040816327 = 1.050574505 Simplifying t + -2.040816327 = 1.050574505 Reorder the terms: -2.040816327 + t = 1.050574505 Solving -2.040816327 + t = 1.050574505 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 = 1.050574505 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = 1.050574505 + 2.040816327 t = 1.050574505 + 2.040816327 Combine like terms: 1.050574505 + 2.040816327 = 3.091390832 t = 3.091390832 Simplifying t = 3.091390832Subproblem 2
t + -2.040816327 = -1.050574505 Simplifying t + -2.040816327 = -1.050574505 Reorder the terms: -2.040816327 + t = -1.050574505 Solving -2.040816327 + t = -1.050574505 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 = -1.050574505 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + t = -1.050574505 + 2.040816327 t = -1.050574505 + 2.040816327 Combine like terms: -1.050574505 + 2.040816327 = 0.990241822 t = 0.990241822 Simplifying t = 0.990241822Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.091390832, 0.990241822}
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