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Simplifying 4.905t2 + 1.6t + -12 = 0 Reorder the terms: -12 + 1.6t + 4.905t2 = 0 Solving -12 + 1.6t + 4.905t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -2.44648318 + 0.3261977574t + t2 = 0 Move the constant term to the right: Add '2.44648318' to each side of the equation. -2.44648318 + 0.3261977574t + 2.44648318 + t2 = 0 + 2.44648318 Reorder the terms: -2.44648318 + 2.44648318 + 0.3261977574t + t2 = 0 + 2.44648318 Combine like terms: -2.44648318 + 2.44648318 = 0.00000000 0.00000000 + 0.3261977574t + t2 = 0 + 2.44648318 0.3261977574t + t2 = 0 + 2.44648318 Combine like terms: 0 + 2.44648318 = 2.44648318 0.3261977574t + t2 = 2.44648318 The t term is 0.3261977574t. Take half its coefficient (0.1630988787). Square it (0.02660124423) and add it to both sides. Add '0.02660124423' to each side of the equation. 0.3261977574t + 0.02660124423 + t2 = 2.44648318 + 0.02660124423 Reorder the terms: 0.02660124423 + 0.3261977574t + t2 = 2.44648318 + 0.02660124423 Combine like terms: 2.44648318 + 0.02660124423 = 2.47308442423 0.02660124423 + 0.3261977574t + t2 = 2.47308442423 Factor a perfect square on the left side: (t + 0.1630988787)(t + 0.1630988787) = 2.47308442423 Calculate the square root of the right side: 1.572604344 Break this problem into two subproblems by setting (t + 0.1630988787) equal to 1.572604344 and -1.572604344.Subproblem 1
t + 0.1630988787 = 1.572604344 Simplifying t + 0.1630988787 = 1.572604344 Reorder the terms: 0.1630988787 + t = 1.572604344 Solving 0.1630988787 + t = 1.572604344 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1630988787' to each side of the equation. 0.1630988787 + -0.1630988787 + t = 1.572604344 + -0.1630988787 Combine like terms: 0.1630988787 + -0.1630988787 = 0.0000000000 0.0000000000 + t = 1.572604344 + -0.1630988787 t = 1.572604344 + -0.1630988787 Combine like terms: 1.572604344 + -0.1630988787 = 1.4095054653 t = 1.4095054653 Simplifying t = 1.4095054653Subproblem 2
t + 0.1630988787 = -1.572604344 Simplifying t + 0.1630988787 = -1.572604344 Reorder the terms: 0.1630988787 + t = -1.572604344 Solving 0.1630988787 + t = -1.572604344 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1630988787' to each side of the equation. 0.1630988787 + -0.1630988787 + t = -1.572604344 + -0.1630988787 Combine like terms: 0.1630988787 + -0.1630988787 = 0.0000000000 0.0000000000 + t = -1.572604344 + -0.1630988787 t = -1.572604344 + -0.1630988787 Combine like terms: -1.572604344 + -0.1630988787 = -1.7357032227 t = -1.7357032227 Simplifying t = -1.7357032227Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.4095054653, -1.7357032227}
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