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Simplifying t2 + -12t + -15.75 = 0 Reorder the terms: -15.75 + -12t + t2 = 0 Solving -15.75 + -12t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '15.75' to each side of the equation. -15.75 + -12t + 15.75 + t2 = 0 + 15.75 Reorder the terms: -15.75 + 15.75 + -12t + t2 = 0 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + -12t + t2 = 0 + 15.75 -12t + t2 = 0 + 15.75 Combine like terms: 0 + 15.75 = 15.75 -12t + t2 = 15.75 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 = 15.75 + 36 Reorder the terms: 36 + -12t + t2 = 15.75 + 36 Combine like terms: 15.75 + 36 = 51.75 36 + -12t + t2 = 51.75 Factor a perfect square on the left side: (t + -6)(t + -6) = 51.75 Calculate the square root of the right side: 7.193747285 Break this problem into two subproblems by setting (t + -6) equal to 7.193747285 and -7.193747285.Subproblem 1
t + -6 = 7.193747285 Simplifying t + -6 = 7.193747285 Reorder the terms: -6 + t = 7.193747285 Solving -6 + t = 7.193747285 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 = 7.193747285 + 6 Combine like terms: -6 + 6 = 0 0 + t = 7.193747285 + 6 t = 7.193747285 + 6 Combine like terms: 7.193747285 + 6 = 13.193747285 t = 13.193747285 Simplifying t = 13.193747285Subproblem 2
t + -6 = -7.193747285 Simplifying t + -6 = -7.193747285 Reorder the terms: -6 + t = -7.193747285 Solving -6 + t = -7.193747285 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 = -7.193747285 + 6 Combine like terms: -6 + 6 = 0 0 + t = -7.193747285 + 6 t = -7.193747285 + 6 Combine like terms: -7.193747285 + 6 = -1.193747285 t = -1.193747285 Simplifying t = -1.193747285Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.193747285, -1.193747285}
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