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Simplifying -1t2 + 16t + 40 = 0 Reorder the terms: 40 + 16t + -1t2 = 0 Solving 40 + 16t + -1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + -16t + t2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -16t + 40 + t2 = 0 + 40 Reorder the terms: -40 + 40 + -16t + t2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -16t + t2 = 0 + 40 -16t + t2 = 0 + 40 Combine like terms: 0 + 40 = 40 -16t + t2 = 40 The t term is -16t. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16t + 64 + t2 = 40 + 64 Reorder the terms: 64 + -16t + t2 = 40 + 64 Combine like terms: 40 + 64 = 104 64 + -16t + t2 = 104 Factor a perfect square on the left side: (t + -8)(t + -8) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (t + -8) equal to 10.198039027 and -10.198039027.Subproblem 1
t + -8 = 10.198039027 Simplifying t + -8 = 10.198039027 Reorder the terms: -8 + t = 10.198039027 Solving -8 + t = 10.198039027 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 10.198039027 + 8 Combine like terms: -8 + 8 = 0 0 + t = 10.198039027 + 8 t = 10.198039027 + 8 Combine like terms: 10.198039027 + 8 = 18.198039027 t = 18.198039027 Simplifying t = 18.198039027Subproblem 2
t + -8 = -10.198039027 Simplifying t + -8 = -10.198039027 Reorder the terms: -8 + t = -10.198039027 Solving -8 + t = -10.198039027 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = -10.198039027 + 8 Combine like terms: -8 + 8 = 0 0 + t = -10.198039027 + 8 t = -10.198039027 + 8 Combine like terms: -10.198039027 + 8 = -2.198039027 t = -2.198039027 Simplifying t = -2.198039027Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.198039027, -2.198039027}
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