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Simplifying 8 = t2 + 5t Reorder the terms: 8 = 5t + t2 Solving 8 = 5t + t2 Solving for variable 't'. Reorder the terms: 8 + -5t + -1t2 = 5t + -5t + t2 + -1t2 Combine like terms: 5t + -5t = 0 8 + -5t + -1t2 = 0 + t2 + -1t2 8 + -5t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 8 + -5t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 5t + t2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 5t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + 5t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5t + t2 = 0 + 8 5t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 5t + t2 = 8 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = 8 + 6.25 Reorder the terms: 6.25 + 5t + t2 = 8 + 6.25 Combine like terms: 8 + 6.25 = 14.25 6.25 + 5t + t2 = 14.25 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (t + 2.5) equal to 3.774917218 and -3.774917218.Subproblem 1
t + 2.5 = 3.774917218 Simplifying t + 2.5 = 3.774917218 Reorder the terms: 2.5 + t = 3.774917218 Solving 2.5 + t = 3.774917218 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 3.774917218 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 3.774917218 + -2.5 t = 3.774917218 + -2.5 Combine like terms: 3.774917218 + -2.5 = 1.274917218 t = 1.274917218 Simplifying t = 1.274917218Subproblem 2
t + 2.5 = -3.774917218 Simplifying t + 2.5 = -3.774917218 Reorder the terms: 2.5 + t = -3.774917218 Solving 2.5 + t = -3.774917218 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -3.774917218 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -3.774917218 + -2.5 t = -3.774917218 + -2.5 Combine like terms: -3.774917218 + -2.5 = -6.274917218 t = -6.274917218 Simplifying t = -6.274917218Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.274917218, -6.274917218}
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