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Simplifying 4.9t2 + 8t + -30 = 0 Reorder the terms: -30 + 8t + 4.9t2 = 0 Solving -30 + 8t + 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'. -6.12244898 + 1.632653061t + t2 = 0 Move the constant term to the right: Add '6.12244898' to each side of the equation. -6.12244898 + 1.632653061t + 6.12244898 + t2 = 0 + 6.12244898 Reorder the terms: -6.12244898 + 6.12244898 + 1.632653061t + t2 = 0 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + 1.632653061t + t2 = 0 + 6.12244898 1.632653061t + t2 = 0 + 6.12244898 Combine like terms: 0 + 6.12244898 = 6.12244898 1.632653061t + t2 = 6.12244898 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 = 6.12244898 + 0.6663890044 Reorder the terms: 0.6663890044 + 1.632653061t + t2 = 6.12244898 + 0.6663890044 Combine like terms: 6.12244898 + 0.6663890044 = 6.7888379844 0.6663890044 + 1.632653061t + t2 = 6.7888379844 Factor a perfect square on the left side: (t + 0.8163265305)(t + 0.8163265305) = 6.7888379844 Calculate the square root of the right side: 2.605539864 Break this problem into two subproblems by setting (t + 0.8163265305) equal to 2.605539864 and -2.605539864.Subproblem 1
t + 0.8163265305 = 2.605539864 Simplifying t + 0.8163265305 = 2.605539864 Reorder the terms: 0.8163265305 + t = 2.605539864 Solving 0.8163265305 + t = 2.605539864 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 = 2.605539864 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + t = 2.605539864 + -0.8163265305 t = 2.605539864 + -0.8163265305 Combine like terms: 2.605539864 + -0.8163265305 = 1.7892133335 t = 1.7892133335 Simplifying t = 1.7892133335Subproblem 2
t + 0.8163265305 = -2.605539864 Simplifying t + 0.8163265305 = -2.605539864 Reorder the terms: 0.8163265305 + t = -2.605539864 Solving 0.8163265305 + t = -2.605539864 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 = -2.605539864 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + t = -2.605539864 + -0.8163265305 t = -2.605539864 + -0.8163265305 Combine like terms: -2.605539864 + -0.8163265305 = -3.4218663945 t = -3.4218663945 Simplifying t = -3.4218663945Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.7892133335, -3.4218663945}
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