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Simplifying t2 + -12t + -36 = 0 Reorder the terms: -36 + -12t + t2 = 0 Solving -36 + -12t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -12t + 36 + t2 = 0 + 36 Reorder the terms: -36 + 36 + -12t + t2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -12t + t2 = 0 + 36 -12t + t2 = 0 + 36 Combine like terms: 0 + 36 = 36 -12t + t2 = 36 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = 36 + 36 Reorder the terms: 36 + -12t + t2 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + -12t + t2 = 72 Factor a perfect square on the left side: (t + -6)(t + -6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (t + -6) equal to 8.485281374 and -8.485281374.Subproblem 1
t + -6 = 8.485281374 Simplifying t + -6 = 8.485281374 Reorder the terms: -6 + t = 8.485281374 Solving -6 + t = 8.485281374 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 8.485281374 + 6 Combine like terms: -6 + 6 = 0 0 + t = 8.485281374 + 6 t = 8.485281374 + 6 Combine like terms: 8.485281374 + 6 = 14.485281374 t = 14.485281374 Simplifying t = 14.485281374Subproblem 2
t + -6 = -8.485281374 Simplifying t + -6 = -8.485281374 Reorder the terms: -6 + t = -8.485281374 Solving -6 + t = -8.485281374 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -8.485281374 + 6 Combine like terms: -6 + 6 = 0 0 + t = -8.485281374 + 6 t = -8.485281374 + 6 Combine like terms: -8.485281374 + 6 = -2.485281374 t = -2.485281374 Simplifying t = -2.485281374Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.485281374, -2.485281374}
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