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Simplifying t2 + -6t + -45 = 0 Reorder the terms: -45 + -6t + t2 = 0 Solving -45 + -6t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -6t + 45 + t2 = 0 + 45 Reorder the terms: -45 + 45 + -6t + t2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -6t + t2 = 0 + 45 -6t + t2 = 0 + 45 Combine like terms: 0 + 45 = 45 -6t + t2 = 45 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 = 45 + 9 Reorder the terms: 9 + -6t + t2 = 45 + 9 Combine like terms: 45 + 9 = 54 9 + -6t + t2 = 54 Factor a perfect square on the left side: (t + -3)(t + -3) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (t + -3) equal to 7.348469228 and -7.348469228.Subproblem 1
t + -3 = 7.348469228 Simplifying t + -3 = 7.348469228 Reorder the terms: -3 + t = 7.348469228 Solving -3 + t = 7.348469228 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 = 7.348469228 + 3 Combine like terms: -3 + 3 = 0 0 + t = 7.348469228 + 3 t = 7.348469228 + 3 Combine like terms: 7.348469228 + 3 = 10.348469228 t = 10.348469228 Simplifying t = 10.348469228Subproblem 2
t + -3 = -7.348469228 Simplifying t + -3 = -7.348469228 Reorder the terms: -3 + t = -7.348469228 Solving -3 + t = -7.348469228 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 = -7.348469228 + 3 Combine like terms: -3 + 3 = 0 0 + t = -7.348469228 + 3 t = -7.348469228 + 3 Combine like terms: -7.348469228 + 3 = -4.348469228 t = -4.348469228 Simplifying t = -4.348469228Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.348469228, -4.348469228}
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