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Simplifying 12 + 18t + -4.905t2 = 0 Solving 12 + 18t + -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 + -3.669724771t + t2 = 0 Move the constant term to the right: Add '2.44648318' to each side of the equation. -2.44648318 + -3.669724771t + 2.44648318 + t2 = 0 + 2.44648318 Reorder the terms: -2.44648318 + 2.44648318 + -3.669724771t + t2 = 0 + 2.44648318 Combine like terms: -2.44648318 + 2.44648318 = 0.00000000 0.00000000 + -3.669724771t + t2 = 0 + 2.44648318 -3.669724771t + t2 = 0 + 2.44648318 Combine like terms: 0 + 2.44648318 = 2.44648318 -3.669724771t + t2 = 2.44648318 The t term is -3.669724771t. Take half its coefficient (-1.834862386). Square it (3.366719976) and add it to both sides. Add '3.366719976' to each side of the equation. -3.669724771t + 3.366719976 + t2 = 2.44648318 + 3.366719976 Reorder the terms: 3.366719976 + -3.669724771t + t2 = 2.44648318 + 3.366719976 Combine like terms: 2.44648318 + 3.366719976 = 5.813203156 3.366719976 + -3.669724771t + t2 = 5.813203156 Factor a perfect square on the left side: (t + -1.834862386)(t + -1.834862386) = 5.813203156 Calculate the square root of the right side: 2.411058514 Break this problem into two subproblems by setting (t + -1.834862386) equal to 2.411058514 and -2.411058514.Subproblem 1
t + -1.834862386 = 2.411058514 Simplifying t + -1.834862386 = 2.411058514 Reorder the terms: -1.834862386 + t = 2.411058514 Solving -1.834862386 + t = 2.411058514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.834862386' to each side of the equation. -1.834862386 + 1.834862386 + t = 2.411058514 + 1.834862386 Combine like terms: -1.834862386 + 1.834862386 = 0.000000000 0.000000000 + t = 2.411058514 + 1.834862386 t = 2.411058514 + 1.834862386 Combine like terms: 2.411058514 + 1.834862386 = 4.2459209 t = 4.2459209 Simplifying t = 4.2459209Subproblem 2
t + -1.834862386 = -2.411058514 Simplifying t + -1.834862386 = -2.411058514 Reorder the terms: -1.834862386 + t = -2.411058514 Solving -1.834862386 + t = -2.411058514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.834862386' to each side of the equation. -1.834862386 + 1.834862386 + t = -2.411058514 + 1.834862386 Combine like terms: -1.834862386 + 1.834862386 = 0.000000000 0.000000000 + t = -2.411058514 + 1.834862386 t = -2.411058514 + 1.834862386 Combine like terms: -2.411058514 + 1.834862386 = -0.576196128 t = -0.576196128 Simplifying t = -0.576196128Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.2459209, -0.576196128}
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