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Simplifying -3t2 + 4t + 9 = 0 Reorder the terms: 9 + 4t + -3t2 = 0 Solving 9 + 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'. -3 + -1.333333333t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.333333333t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + -1.333333333t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.333333333t + t2 = 0 + 3 -1.333333333t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.333333333t + t2 = 3 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 = 3 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333t + t2 = 3 + 0.4444444442 Combine like terms: 3 + 0.4444444442 = 3.4444444442 0.4444444442 + -1.333333333t + t2 = 3.4444444442 Factor a perfect square on the left side: (t + -0.6666666665)(t + -0.6666666665) = 3.4444444442 Calculate the square root of the right side: 1.855921454 Break this problem into two subproblems by setting (t + -0.6666666665) equal to 1.855921454 and -1.855921454.Subproblem 1
t + -0.6666666665 = 1.855921454 Simplifying t + -0.6666666665 = 1.855921454 Reorder the terms: -0.6666666665 + t = 1.855921454 Solving -0.6666666665 + t = 1.855921454 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 = 1.855921454 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + t = 1.855921454 + 0.6666666665 t = 1.855921454 + 0.6666666665 Combine like terms: 1.855921454 + 0.6666666665 = 2.5225881205 t = 2.5225881205 Simplifying t = 2.5225881205Subproblem 2
t + -0.6666666665 = -1.855921454 Simplifying t + -0.6666666665 = -1.855921454 Reorder the terms: -0.6666666665 + t = -1.855921454 Solving -0.6666666665 + t = -1.855921454 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 = -1.855921454 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + t = -1.855921454 + 0.6666666665 t = -1.855921454 + 0.6666666665 Combine like terms: -1.855921454 + 0.6666666665 = -1.1892547875 t = -1.1892547875 Simplifying t = -1.1892547875Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.5225881205, -1.1892547875}
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