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Simplifying t2 + 8t + 16 = 45 Reorder the terms: 16 + 8t + t2 = 45 Solving 16 + 8t + t2 = 45 Solving for variable 't'. Reorder the terms: 16 + -45 + 8t + t2 = 45 + -45 Combine like terms: 16 + -45 = -29 -29 + 8t + t2 = 45 + -45 Combine like terms: 45 + -45 = 0 -29 + 8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 8t + 29 + t2 = 0 + 29 Reorder the terms: -29 + 29 + 8t + t2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 8t + t2 = 0 + 29 8t + t2 = 0 + 29 Combine like terms: 0 + 29 = 29 8t + t2 = 29 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 = 29 + 16 Reorder the terms: 16 + 8t + t2 = 29 + 16 Combine like terms: 29 + 16 = 45 16 + 8t + t2 = 45 Factor a perfect square on the left side: (t + 4)(t + 4) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (t + 4) equal to 6.708203933 and -6.708203933.Subproblem 1
t + 4 = 6.708203933 Simplifying t + 4 = 6.708203933 Reorder the terms: 4 + t = 6.708203933 Solving 4 + t = 6.708203933 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 = 6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + t = 6.708203933 + -4 t = 6.708203933 + -4 Combine like terms: 6.708203933 + -4 = 2.708203933 t = 2.708203933 Simplifying t = 2.708203933Subproblem 2
t + 4 = -6.708203933 Simplifying t + 4 = -6.708203933 Reorder the terms: 4 + t = -6.708203933 Solving 4 + t = -6.708203933 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 = -6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + t = -6.708203933 + -4 t = -6.708203933 + -4 Combine like terms: -6.708203933 + -4 = -10.708203933 t = -10.708203933 Simplifying t = -10.708203933Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.708203933, -10.708203933}
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