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Simplifying 0 = -3t2 + 30t + -29 Reorder the terms: 0 = -29 + 30t + -3t2 Solving 0 = -29 + 30t + -3t2 Solving for variable 't'. Combine like terms: 0 + 29 = 29 29 + -30t + 3t2 = -29 + 30t + -3t2 + 29 + -30t + 3t2 Reorder the terms: 29 + -30t + 3t2 = -29 + 29 + 30t + -30t + -3t2 + 3t2 Combine like terms: -29 + 29 = 0 29 + -30t + 3t2 = 0 + 30t + -30t + -3t2 + 3t2 29 + -30t + 3t2 = 30t + -30t + -3t2 + 3t2 Combine like terms: 30t + -30t = 0 29 + -30t + 3t2 = 0 + -3t2 + 3t2 29 + -30t + 3t2 = -3t2 + 3t2 Combine like terms: -3t2 + 3t2 = 0 29 + -30t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 9.666666667 + -10t + t2 = 0 Move the constant term to the right: Add '-9.666666667' to each side of the equation. 9.666666667 + -10t + -9.666666667 + t2 = 0 + -9.666666667 Reorder the terms: 9.666666667 + -9.666666667 + -10t + t2 = 0 + -9.666666667 Combine like terms: 9.666666667 + -9.666666667 = 0.000000000 0.000000000 + -10t + t2 = 0 + -9.666666667 -10t + t2 = 0 + -9.666666667 Combine like terms: 0 + -9.666666667 = -9.666666667 -10t + t2 = -9.666666667 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -9.666666667 + 25 Reorder the terms: 25 + -10t + t2 = -9.666666667 + 25 Combine like terms: -9.666666667 + 25 = 15.333333333 25 + -10t + t2 = 15.333333333 Factor a perfect square on the left side: (t + -5)(t + -5) = 15.333333333 Calculate the square root of the right side: 3.915780041 Break this problem into two subproblems by setting (t + -5) equal to 3.915780041 and -3.915780041.Subproblem 1
t + -5 = 3.915780041 Simplifying t + -5 = 3.915780041 Reorder the terms: -5 + t = 3.915780041 Solving -5 + t = 3.915780041 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 3.915780041 + 5 Combine like terms: -5 + 5 = 0 0 + t = 3.915780041 + 5 t = 3.915780041 + 5 Combine like terms: 3.915780041 + 5 = 8.915780041 t = 8.915780041 Simplifying t = 8.915780041Subproblem 2
t + -5 = -3.915780041 Simplifying t + -5 = -3.915780041 Reorder the terms: -5 + t = -3.915780041 Solving -5 + t = -3.915780041 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -3.915780041 + 5 Combine like terms: -5 + 5 = 0 0 + t = -3.915780041 + 5 t = -3.915780041 + 5 Combine like terms: -3.915780041 + 5 = 1.084219959 t = 1.084219959 Simplifying t = 1.084219959Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.915780041, 1.084219959}
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