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Simplifying t2 + 10t = -22 Reorder the terms: 10t + t2 = -22 Solving 10t + t2 = -22 Solving for variable 't'. Reorder the terms: 22 + 10t + t2 = -22 + 22 Combine like terms: -22 + 22 = 0 22 + 10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 10t + -22 + t2 = 0 + -22 Reorder the terms: 22 + -22 + 10t + t2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 10t + t2 = 0 + -22 10t + t2 = 0 + -22 Combine like terms: 0 + -22 = -22 10t + t2 = -22 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = -22 + 25 Reorder the terms: 25 + 10t + t2 = -22 + 25 Combine like terms: -22 + 25 = 3 25 + 10t + t2 = 3 Factor a perfect square on the left side: (t + 5)(t + 5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (t + 5) equal to 1.732050808 and -1.732050808.Subproblem 1
t + 5 = 1.732050808 Simplifying t + 5 = 1.732050808 Reorder the terms: 5 + t = 1.732050808 Solving 5 + t = 1.732050808 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 1.732050808 + -5 Combine like terms: 5 + -5 = 0 0 + t = 1.732050808 + -5 t = 1.732050808 + -5 Combine like terms: 1.732050808 + -5 = -3.267949192 t = -3.267949192 Simplifying t = -3.267949192Subproblem 2
t + 5 = -1.732050808 Simplifying t + 5 = -1.732050808 Reorder the terms: 5 + t = -1.732050808 Solving 5 + t = -1.732050808 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -1.732050808 + -5 Combine like terms: 5 + -5 = 0 0 + t = -1.732050808 + -5 t = -1.732050808 + -5 Combine like terms: -1.732050808 + -5 = -6.732050808 t = -6.732050808 Simplifying t = -6.732050808Solution
The solution to the problem is based on the solutions from the subproblems. t = {-3.267949192, -6.732050808}
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