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Simplifying 4.9t2 + -15t + -76 = 0 Reorder the terms: -76 + -15t + 4.9t2 = 0 Solving -76 + -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'. -15.51020408 + -3.06122449t + t2 = 0 Move the constant term to the right: Add '15.51020408' to each side of the equation. -15.51020408 + -3.06122449t + 15.51020408 + t2 = 0 + 15.51020408 Reorder the terms: -15.51020408 + 15.51020408 + -3.06122449t + t2 = 0 + 15.51020408 Combine like terms: -15.51020408 + 15.51020408 = 0.00000000 0.00000000 + -3.06122449t + t2 = 0 + 15.51020408 -3.06122449t + t2 = 0 + 15.51020408 Combine like terms: 0 + 15.51020408 = 15.51020408 -3.06122449t + t2 = 15.51020408 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 = 15.51020408 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449t + t2 = 15.51020408 + 2.342773845 Combine like terms: 15.51020408 + 2.342773845 = 17.852977925 2.342773845 + -3.06122449t + t2 = 17.852977925 Factor a perfect square on the left side: (t + -1.530612245)(t + -1.530612245) = 17.852977925 Calculate the square root of the right side: 4.225278443 Break this problem into two subproblems by setting (t + -1.530612245) equal to 4.225278443 and -4.225278443.Subproblem 1
t + -1.530612245 = 4.225278443 Simplifying t + -1.530612245 = 4.225278443 Reorder the terms: -1.530612245 + t = 4.225278443 Solving -1.530612245 + t = 4.225278443 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 = 4.225278443 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = 4.225278443 + 1.530612245 t = 4.225278443 + 1.530612245 Combine like terms: 4.225278443 + 1.530612245 = 5.755890688 t = 5.755890688 Simplifying t = 5.755890688Subproblem 2
t + -1.530612245 = -4.225278443 Simplifying t + -1.530612245 = -4.225278443 Reorder the terms: -1.530612245 + t = -4.225278443 Solving -1.530612245 + t = -4.225278443 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 = -4.225278443 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + t = -4.225278443 + 1.530612245 t = -4.225278443 + 1.530612245 Combine like terms: -4.225278443 + 1.530612245 = -2.694666198 t = -2.694666198 Simplifying t = -2.694666198Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.755890688, -2.694666198}
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