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Simplifying 3t2 + -4t + -12 = 0 Reorder the terms: -12 + -4t + 3t2 = 0 Solving -12 + -4t + 3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + -1.333333333t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.333333333t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -1.333333333t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.333333333t + t2 = 0 + 4 -1.333333333t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.333333333t + t2 = 4 The t term is -1.333333333t. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333t + 0.4444444442 + t2 = 4 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333t + t2 = 4 + 0.4444444442 Combine like terms: 4 + 0.4444444442 = 4.4444444442 0.4444444442 + -1.333333333t + t2 = 4.4444444442 Factor a perfect square on the left side: (t + -0.6666666665)(t + -0.6666666665) = 4.4444444442 Calculate the square root of the right side: 2.108185107 Break this problem into two subproblems by setting (t + -0.6666666665) equal to 2.108185107 and -2.108185107.Subproblem 1
t + -0.6666666665 = 2.108185107 Simplifying t + -0.6666666665 = 2.108185107 Reorder the terms: -0.6666666665 + t = 2.108185107 Solving -0.6666666665 + t = 2.108185107 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + t = 2.108185107 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + t = 2.108185107 + 0.6666666665 t = 2.108185107 + 0.6666666665 Combine like terms: 2.108185107 + 0.6666666665 = 2.7748517735 t = 2.7748517735 Simplifying t = 2.7748517735Subproblem 2
t + -0.6666666665 = -2.108185107 Simplifying t + -0.6666666665 = -2.108185107 Reorder the terms: -0.6666666665 + t = -2.108185107 Solving -0.6666666665 + t = -2.108185107 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + t = -2.108185107 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + t = -2.108185107 + 0.6666666665 t = -2.108185107 + 0.6666666665 Combine like terms: -2.108185107 + 0.6666666665 = -1.4415184405 t = -1.4415184405 Simplifying t = -1.4415184405Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.7748517735, -1.4415184405}
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