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Simplifying 0 = 1.2t2 + -20.08t + 4.8 Reorder the terms: 0 = 4.8 + -20.08t + 1.2t2 Solving 0 = 4.8 + -20.08t + 1.2t2 Solving for variable 't'. Combine like terms: 0 + -4.8 = -4.8 -4.8 + 20.08t + -1.2t2 = 4.8 + -20.08t + 1.2t2 + -4.8 + 20.08t + -1.2t2 Reorder the terms: -4.8 + 20.08t + -1.2t2 = 4.8 + -4.8 + -20.08t + 20.08t + 1.2t2 + -1.2t2 Combine like terms: 4.8 + -4.8 = 0.0 -4.8 + 20.08t + -1.2t2 = 0.0 + -20.08t + 20.08t + 1.2t2 + -1.2t2 -4.8 + 20.08t + -1.2t2 = -20.08t + 20.08t + 1.2t2 + -1.2t2 Combine like terms: -20.08t + 20.08t = 0.00 -4.8 + 20.08t + -1.2t2 = 0.00 + 1.2t2 + -1.2t2 -4.8 + 20.08t + -1.2t2 = 1.2t2 + -1.2t2 Combine like terms: 1.2t2 + -1.2t2 = 0.0 -4.8 + 20.08t + -1.2t2 = 0.0 Begin completing the square. Divide all terms by -1.2 the coefficient of the squared term: Divide each side by '-1.2'. 4 + -16.73333333t + t2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -16.73333333t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + -16.73333333t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -16.73333333t + t2 = 0 + -4 -16.73333333t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 -16.73333333t + t2 = -4 The t term is -16.73333333t. Take half its coefficient (-8.366666665). Square it (70.00111108) and add it to both sides. Add '70.00111108' to each side of the equation. -16.73333333t + 70.00111108 + t2 = -4 + 70.00111108 Reorder the terms: 70.00111108 + -16.73333333t + t2 = -4 + 70.00111108 Combine like terms: -4 + 70.00111108 = 66.00111108 70.00111108 + -16.73333333t + t2 = 66.00111108 Factor a perfect square on the left side: (t + -8.366666665)(t + -8.366666665) = 66.00111108 Calculate the square root of the right side: 8.124106787 Break this problem into two subproblems by setting (t + -8.366666665) equal to 8.124106787 and -8.124106787.Subproblem 1
t + -8.366666665 = 8.124106787 Simplifying t + -8.366666665 = 8.124106787 Reorder the terms: -8.366666665 + t = 8.124106787 Solving -8.366666665 + t = 8.124106787 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.366666665' to each side of the equation. -8.366666665 + 8.366666665 + t = 8.124106787 + 8.366666665 Combine like terms: -8.366666665 + 8.366666665 = 0.000000000 0.000000000 + t = 8.124106787 + 8.366666665 t = 8.124106787 + 8.366666665 Combine like terms: 8.124106787 + 8.366666665 = 16.490773452 t = 16.490773452 Simplifying t = 16.490773452Subproblem 2
t + -8.366666665 = -8.124106787 Simplifying t + -8.366666665 = -8.124106787 Reorder the terms: -8.366666665 + t = -8.124106787 Solving -8.366666665 + t = -8.124106787 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.366666665' to each side of the equation. -8.366666665 + 8.366666665 + t = -8.124106787 + 8.366666665 Combine like terms: -8.366666665 + 8.366666665 = 0.000000000 0.000000000 + t = -8.124106787 + 8.366666665 t = -8.124106787 + 8.366666665 Combine like terms: -8.124106787 + 8.366666665 = 0.242559878 t = 0.242559878 Simplifying t = 0.242559878Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.490773452, 0.242559878}
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