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Simplifying 0 = -4.9t2 + 8t + 12 Reorder the terms: 0 = 12 + 8t + -4.9t2 Solving 0 = 12 + 8t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + -8t + 4.9t2 = 12 + 8t + -4.9t2 + -12 + -8t + 4.9t2 Reorder the terms: -12 + -8t + 4.9t2 = 12 + -12 + 8t + -8t + -4.9t2 + 4.9t2 Combine like terms: 12 + -12 = 0 -12 + -8t + 4.9t2 = 0 + 8t + -8t + -4.9t2 + 4.9t2 -12 + -8t + 4.9t2 = 8t + -8t + -4.9t2 + 4.9t2 Combine like terms: 8t + -8t = 0 -12 + -8t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -12 + -8t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -12 + -8t + 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'. -2.448979592 + -1.632653061t + t2 = 0 Move the constant term to the right: Add '2.448979592' to each side of the equation. -2.448979592 + -1.632653061t + 2.448979592 + t2 = 0 + 2.448979592 Reorder the terms: -2.448979592 + 2.448979592 + -1.632653061t + t2 = 0 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + -1.632653061t + t2 = 0 + 2.448979592 -1.632653061t + t2 = 0 + 2.448979592 Combine like terms: 0 + 2.448979592 = 2.448979592 -1.632653061t + t2 = 2.448979592 The t term is -1.632653061t. Take half its coefficient (-0.8163265305). Square it (0.6663890044) and add it to both sides. Add '0.6663890044' to each side of the equation. -1.632653061t + 0.6663890044 + t2 = 2.448979592 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061t + t2 = 2.448979592 + 0.6663890044 Combine like terms: 2.448979592 + 0.6663890044 = 3.1153685964 0.6663890044 + -1.632653061t + t2 = 3.1153685964 Factor a perfect square on the left side: (t + -0.8163265305)(t + -0.8163265305) = 3.1153685964 Calculate the square root of the right side: 1.765040678 Break this problem into two subproblems by setting (t + -0.8163265305) equal to 1.765040678 and -1.765040678.Subproblem 1
t + -0.8163265305 = 1.765040678 Simplifying t + -0.8163265305 = 1.765040678 Reorder the terms: -0.8163265305 + t = 1.765040678 Solving -0.8163265305 + t = 1.765040678 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + t = 1.765040678 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + t = 1.765040678 + 0.8163265305 t = 1.765040678 + 0.8163265305 Combine like terms: 1.765040678 + 0.8163265305 = 2.5813672085 t = 2.5813672085 Simplifying t = 2.5813672085Subproblem 2
t + -0.8163265305 = -1.765040678 Simplifying t + -0.8163265305 = -1.765040678 Reorder the terms: -0.8163265305 + t = -1.765040678 Solving -0.8163265305 + t = -1.765040678 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + t = -1.765040678 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + t = -1.765040678 + 0.8163265305 t = -1.765040678 + 0.8163265305 Combine like terms: -1.765040678 + 0.8163265305 = -0.9487141475 t = -0.9487141475 Simplifying t = -0.9487141475Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.5813672085, -0.9487141475}
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