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Simplifying -4.9t2 + 5.5t + 105 = 0 Reorder the terms: 105 + 5.5t + -4.9t2 = 0 Solving 105 + 5.5t + -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'. -21.42857143 + -1.12244898t + t2 = 0 Move the constant term to the right: Add '21.42857143' to each side of the equation. -21.42857143 + -1.12244898t + 21.42857143 + t2 = 0 + 21.42857143 Reorder the terms: -21.42857143 + 21.42857143 + -1.12244898t + t2 = 0 + 21.42857143 Combine like terms: -21.42857143 + 21.42857143 = 0.00000000 0.00000000 + -1.12244898t + t2 = 0 + 21.42857143 -1.12244898t + t2 = 0 + 21.42857143 Combine like terms: 0 + 21.42857143 = 21.42857143 -1.12244898t + t2 = 21.42857143 The t term is -1.12244898t. Take half its coefficient (-0.56122449). Square it (0.3149729282) and add it to both sides. Add '0.3149729282' to each side of the equation. -1.12244898t + 0.3149729282 + t2 = 21.42857143 + 0.3149729282 Reorder the terms: 0.3149729282 + -1.12244898t + t2 = 21.42857143 + 0.3149729282 Combine like terms: 21.42857143 + 0.3149729282 = 21.7435443582 0.3149729282 + -1.12244898t + t2 = 21.7435443582 Factor a perfect square on the left side: (t + -0.56122449)(t + -0.56122449) = 21.7435443582 Calculate the square root of the right side: 4.662997358 Break this problem into two subproblems by setting (t + -0.56122449) equal to 4.662997358 and -4.662997358.Subproblem 1
t + -0.56122449 = 4.662997358 Simplifying t + -0.56122449 = 4.662997358 Reorder the terms: -0.56122449 + t = 4.662997358 Solving -0.56122449 + t = 4.662997358 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + t = 4.662997358 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + t = 4.662997358 + 0.56122449 t = 4.662997358 + 0.56122449 Combine like terms: 4.662997358 + 0.56122449 = 5.224221848 t = 5.224221848 Simplifying t = 5.224221848Subproblem 2
t + -0.56122449 = -4.662997358 Simplifying t + -0.56122449 = -4.662997358 Reorder the terms: -0.56122449 + t = -4.662997358 Solving -0.56122449 + t = -4.662997358 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + t = -4.662997358 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + t = -4.662997358 + 0.56122449 t = -4.662997358 + 0.56122449 Combine like terms: -4.662997358 + 0.56122449 = -4.101772868 t = -4.101772868 Simplifying t = -4.101772868Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.224221848, -4.101772868}
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