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Simplifying t2 + 3t + 3t + 9 = 5 Reorder the terms: 9 + 3t + 3t + t2 = 5 Combine like terms: 3t + 3t = 6t 9 + 6t + t2 = 5 Solving 9 + 6t + t2 = 5 Solving for variable 't'. Reorder the terms: 9 + -5 + 6t + t2 = 5 + -5 Combine like terms: 9 + -5 = 4 4 + 6t + t2 = 5 + -5 Combine like terms: 5 + -5 = 0 4 + 6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 6t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + 6t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6t + t2 = 0 + -4 6t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 6t + t2 = -4 The t term is 6t. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t + 9 + t2 = -4 + 9 Reorder the terms: 9 + 6t + t2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + 6t + t2 = 5 Factor a perfect square on the left side: (t + 3)(t + 3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (t + 3) equal to 2.236067978 and -2.236067978.Subproblem 1
t + 3 = 2.236067978 Simplifying t + 3 = 2.236067978 Reorder the terms: 3 + t = 2.236067978 Solving 3 + t = 2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + t = 2.236067978 + -3 t = 2.236067978 + -3 Combine like terms: 2.236067978 + -3 = -0.763932022 t = -0.763932022 Simplifying t = -0.763932022Subproblem 2
t + 3 = -2.236067978 Simplifying t + 3 = -2.236067978 Reorder the terms: 3 + t = -2.236067978 Solving 3 + t = -2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = -2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + t = -2.236067978 + -3 t = -2.236067978 + -3 Combine like terms: -2.236067978 + -3 = -5.236067978 t = -5.236067978 Simplifying t = -5.236067978Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.763932022, -5.236067978}
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