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Simplifying 0 = 8 + 40.8t + -16t2 Solving 0 = 8 + 40.8t + -16t2 Solving for variable 't'. Combine like terms: 0 + -8 = -8 -8 + -40.8t + 16t2 = 8 + 40.8t + -16t2 + -8 + -40.8t + 16t2 Reorder the terms: -8 + -40.8t + 16t2 = 8 + -8 + 40.8t + -40.8t + -16t2 + 16t2 Combine like terms: 8 + -8 = 0 -8 + -40.8t + 16t2 = 0 + 40.8t + -40.8t + -16t2 + 16t2 -8 + -40.8t + 16t2 = 40.8t + -40.8t + -16t2 + 16t2 Combine like terms: 40.8t + -40.8t = 0.0 -8 + -40.8t + 16t2 = 0.0 + -16t2 + 16t2 -8 + -40.8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -8 + -40.8t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5 + -2.55t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.55t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.55t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.55t + t2 = 0 + 0.5 -2.55t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.55t + t2 = 0.5 The t term is -2.55t. Take half its coefficient (-1.275). Square it (1.625625) and add it to both sides. Add '1.625625' to each side of the equation. -2.55t + 1.625625 + t2 = 0.5 + 1.625625 Reorder the terms: 1.625625 + -2.55t + t2 = 0.5 + 1.625625 Combine like terms: 0.5 + 1.625625 = 2.125625 1.625625 + -2.55t + t2 = 2.125625 Factor a perfect square on the left side: (t + -1.275)(t + -1.275) = 2.125625 Calculate the square root of the right side: 1.457952331 Break this problem into two subproblems by setting (t + -1.275) equal to 1.457952331 and -1.457952331.Subproblem 1
t + -1.275 = 1.457952331 Simplifying t + -1.275 = 1.457952331 Reorder the terms: -1.275 + t = 1.457952331 Solving -1.275 + t = 1.457952331 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.275' to each side of the equation. -1.275 + 1.275 + t = 1.457952331 + 1.275 Combine like terms: -1.275 + 1.275 = 0.000 0.000 + t = 1.457952331 + 1.275 t = 1.457952331 + 1.275 Combine like terms: 1.457952331 + 1.275 = 2.732952331 t = 2.732952331 Simplifying t = 2.732952331Subproblem 2
t + -1.275 = -1.457952331 Simplifying t + -1.275 = -1.457952331 Reorder the terms: -1.275 + t = -1.457952331 Solving -1.275 + t = -1.457952331 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.275' to each side of the equation. -1.275 + 1.275 + t = -1.457952331 + 1.275 Combine like terms: -1.275 + 1.275 = 0.000 0.000 + t = -1.457952331 + 1.275 t = -1.457952331 + 1.275 Combine like terms: -1.457952331 + 1.275 = -0.182952331 t = -0.182952331 Simplifying t = -0.182952331Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.732952331, -0.182952331}
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