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Simplifying 0 = t2 + -8t + 6 Reorder the terms: 0 = 6 + -8t + t2 Solving 0 = 6 + -8t + t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + 8t + -1t2 = 6 + -8t + t2 + -6 + 8t + -1t2 Reorder the terms: -6 + 8t + -1t2 = 6 + -6 + -8t + 8t + t2 + -1t2 Combine like terms: 6 + -6 = 0 -6 + 8t + -1t2 = 0 + -8t + 8t + t2 + -1t2 -6 + 8t + -1t2 = -8t + 8t + t2 + -1t2 Combine like terms: -8t + 8t = 0 -6 + 8t + -1t2 = 0 + t2 + -1t2 -6 + 8t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 -6 + 8t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -8t + t2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -8t + -6 + t2 = 0 + -6 Reorder the terms: 6 + -6 + -8t + t2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -8t + t2 = 0 + -6 -8t + t2 = 0 + -6 Combine like terms: 0 + -6 = -6 -8t + t2 = -6 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -6 + 16 Reorder the terms: 16 + -8t + t2 = -6 + 16 Combine like terms: -6 + 16 = 10 16 + -8t + t2 = 10 Factor a perfect square on the left side: (t + -4)(t + -4) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (t + -4) equal to 3.16227766 and -3.16227766.Subproblem 1
t + -4 = 3.16227766 Simplifying t + -4 = 3.16227766 Reorder the terms: -4 + t = 3.16227766 Solving -4 + t = 3.16227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.16227766 + 4 t = 3.16227766 + 4 Combine like terms: 3.16227766 + 4 = 7.16227766 t = 7.16227766 Simplifying t = 7.16227766Subproblem 2
t + -4 = -3.16227766 Simplifying t + -4 = -3.16227766 Reorder the terms: -4 + t = -3.16227766 Solving -4 + t = -3.16227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.16227766 + 4 t = -3.16227766 + 4 Combine like terms: -3.16227766 + 4 = 0.83772234 t = 0.83772234 Simplifying t = 0.83772234Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.16227766, 0.83772234}
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