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Simplifying 72 + -4.9t2 = 8t Solving 72 + -4.9t2 = 8t Solving for variable 't'. Reorder the terms: 72 + -8t + -4.9t2 = 8t + -8t Combine like terms: 8t + -8t = 0 72 + -8t + -4.9t2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -14.69387755 + 1.632653061t + t2 = 0 Move the constant term to the right: Add '14.69387755' to each side of the equation. -14.69387755 + 1.632653061t + 14.69387755 + t2 = 0 + 14.69387755 Reorder the terms: -14.69387755 + 14.69387755 + 1.632653061t + t2 = 0 + 14.69387755 Combine like terms: -14.69387755 + 14.69387755 = 0.00000000 0.00000000 + 1.632653061t + t2 = 0 + 14.69387755 1.632653061t + t2 = 0 + 14.69387755 Combine like terms: 0 + 14.69387755 = 14.69387755 1.632653061t + t2 = 14.69387755 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 = 14.69387755 + 0.6663890044 Reorder the terms: 0.6663890044 + 1.632653061t + t2 = 14.69387755 + 0.6663890044 Combine like terms: 14.69387755 + 0.6663890044 = 15.3602665544 0.6663890044 + 1.632653061t + t2 = 15.3602665544 Factor a perfect square on the left side: (t + 0.8163265305)(t + 0.8163265305) = 15.3602665544 Calculate the square root of the right side: 3.919217595 Break this problem into two subproblems by setting (t + 0.8163265305) equal to 3.919217595 and -3.919217595.Subproblem 1
t + 0.8163265305 = 3.919217595 Simplifying t + 0.8163265305 = 3.919217595 Reorder the terms: 0.8163265305 + t = 3.919217595 Solving 0.8163265305 + t = 3.919217595 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 = 3.919217595 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + t = 3.919217595 + -0.8163265305 t = 3.919217595 + -0.8163265305 Combine like terms: 3.919217595 + -0.8163265305 = 3.1028910645 t = 3.1028910645 Simplifying t = 3.1028910645Subproblem 2
t + 0.8163265305 = -3.919217595 Simplifying t + 0.8163265305 = -3.919217595 Reorder the terms: 0.8163265305 + t = -3.919217595 Solving 0.8163265305 + t = -3.919217595 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 = -3.919217595 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + t = -3.919217595 + -0.8163265305 t = -3.919217595 + -0.8163265305 Combine like terms: -3.919217595 + -0.8163265305 = -4.7355441255 t = -4.7355441255 Simplifying t = -4.7355441255Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.1028910645, -4.7355441255}
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