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Simplifying t2 + -3t + -6 = 5 Reorder the terms: -6 + -3t + t2 = 5 Solving -6 + -3t + t2 = 5 Solving for variable 't'. Reorder the terms: -6 + -5 + -3t + t2 = 5 + -5 Combine like terms: -6 + -5 = -11 -11 + -3t + t2 = 5 + -5 Combine like terms: 5 + -5 = 0 -11 + -3t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -3t + 11 + t2 = 0 + 11 Reorder the terms: -11 + 11 + -3t + t2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -3t + t2 = 0 + 11 -3t + t2 = 0 + 11 Combine like terms: 0 + 11 = 11 -3t + t2 = 11 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 11 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 11 + 2.25 Combine like terms: 11 + 2.25 = 13.25 2.25 + -3t + t2 = 13.25 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (t + -1.5) equal to 3.640054945 and -3.640054945.Subproblem 1
t + -1.5 = 3.640054945 Simplifying t + -1.5 = 3.640054945 Reorder the terms: -1.5 + t = 3.640054945 Solving -1.5 + t = 3.640054945 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 3.640054945 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 3.640054945 + 1.5 t = 3.640054945 + 1.5 Combine like terms: 3.640054945 + 1.5 = 5.140054945 t = 5.140054945 Simplifying t = 5.140054945Subproblem 2
t + -1.5 = -3.640054945 Simplifying t + -1.5 = -3.640054945 Reorder the terms: -1.5 + t = -3.640054945 Solving -1.5 + t = -3.640054945 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -3.640054945 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -3.640054945 + 1.5 t = -3.640054945 + 1.5 Combine like terms: -3.640054945 + 1.5 = -2.140054945 t = -2.140054945 Simplifying t = -2.140054945Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.140054945, -2.140054945}
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