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Simplifying -4.9t2 + 15t + 1 = 0 Reorder the terms: 1 + 15t + -4.9t2 = 0 Solving 1 + 15t + -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'. -0.2040816327 + -3.06122449t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -3.06122449t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -3.06122449t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -3.06122449t + t2 = 0 + 0.2040816327 -3.06122449t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -3.06122449t + t2 = 0.2040816327 The t term is -3.06122449t. Take half its coefficient (-1.530612245). Square it (2.342773845) and add it to both sides. Add '2.342773845' to each side of the equation. -3.06122449t + 2.342773845 + t2 = 0.2040816327 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449t + t2 = 0.2040816327 + 2.342773845 Combine like terms: 0.2040816327 + 2.342773845 = 2.5468554777 2.342773845 + -3.06122449t + t2 = 2.5468554777 Factor a perfect square on the left side: (t + -1.530612245)(t + -1.530612245) = 2.5468554777 Calculate the square root of the right side: 1.59588705 Break this problem into two subproblems by setting (t + -1.530612245) equal to 1.59588705 and -1.59588705.Subproblem 1
t + -1.530612245 = 1.59588705 Simplifying t + -1.530612245 = 1.59588705 Reorder the terms: -1.530612245 + t = 1.59588705 Solving -1.530612245 + t = 1.59588705 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.530612245' to each side of the equation. -1.530612245 + 1.530612245 + t = 1.59588705 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = 1.59588705 + 1.530612245 t = 1.59588705 + 1.530612245 Combine like terms: 1.59588705 + 1.530612245 = 3.126499295 t = 3.126499295 Simplifying t = 3.126499295Subproblem 2
t + -1.530612245 = -1.59588705 Simplifying t + -1.530612245 = -1.59588705 Reorder the terms: -1.530612245 + t = -1.59588705 Solving -1.530612245 + t = -1.59588705 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.530612245' to each side of the equation. -1.530612245 + 1.530612245 + t = -1.59588705 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = -1.59588705 + 1.530612245 t = -1.59588705 + 1.530612245 Combine like terms: -1.59588705 + 1.530612245 = -0.065274805 t = -0.065274805 Simplifying t = -0.065274805Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.126499295, -0.065274805}
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