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Simplifying t2 + -12t + -18 = 0 Reorder the terms: -18 + -12t + t2 = 0 Solving -18 + -12t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -12t + 18 + t2 = 0 + 18 Reorder the terms: -18 + 18 + -12t + t2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -12t + t2 = 0 + 18 -12t + t2 = 0 + 18 Combine like terms: 0 + 18 = 18 -12t + t2 = 18 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 = 18 + 36 Reorder the terms: 36 + -12t + t2 = 18 + 36 Combine like terms: 18 + 36 = 54 36 + -12t + t2 = 54 Factor a perfect square on the left side: (t + -6)(t + -6) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (t + -6) equal to 7.348469228 and -7.348469228.Subproblem 1
t + -6 = 7.348469228 Simplifying t + -6 = 7.348469228 Reorder the terms: -6 + t = 7.348469228 Solving -6 + t = 7.348469228 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 = 7.348469228 + 6 Combine like terms: -6 + 6 = 0 0 + t = 7.348469228 + 6 t = 7.348469228 + 6 Combine like terms: 7.348469228 + 6 = 13.348469228 t = 13.348469228 Simplifying t = 13.348469228Subproblem 2
t + -6 = -7.348469228 Simplifying t + -6 = -7.348469228 Reorder the terms: -6 + t = -7.348469228 Solving -6 + t = -7.348469228 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 = -7.348469228 + 6 Combine like terms: -6 + 6 = 0 0 + t = -7.348469228 + 6 t = -7.348469228 + 6 Combine like terms: -7.348469228 + 6 = -1.348469228 t = -1.348469228 Simplifying t = -1.348469228Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.348469228, -1.348469228}
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