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Simplifying 4800 = 3t2 + -13t + 18 Reorder the terms: 4800 = 18 + -13t + 3t2 Solving 4800 = 18 + -13t + 3t2 Solving for variable 't'. Combine like terms: 4800 + -18 = 4782 4782 + 13t + -3t2 = 18 + -13t + 3t2 + -18 + 13t + -3t2 Reorder the terms: 4782 + 13t + -3t2 = 18 + -18 + -13t + 13t + 3t2 + -3t2 Combine like terms: 18 + -18 = 0 4782 + 13t + -3t2 = 0 + -13t + 13t + 3t2 + -3t2 4782 + 13t + -3t2 = -13t + 13t + 3t2 + -3t2 Combine like terms: -13t + 13t = 0 4782 + 13t + -3t2 = 0 + 3t2 + -3t2 4782 + 13t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 4782 + 13t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1594 + -4.333333333t + t2 = 0 Move the constant term to the right: Add '1594' to each side of the equation. -1594 + -4.333333333t + 1594 + t2 = 0 + 1594 Reorder the terms: -1594 + 1594 + -4.333333333t + t2 = 0 + 1594 Combine like terms: -1594 + 1594 = 0 0 + -4.333333333t + t2 = 0 + 1594 -4.333333333t + t2 = 0 + 1594 Combine like terms: 0 + 1594 = 1594 -4.333333333t + t2 = 1594 The t term is -4.333333333t. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333t + 4.694444446 + t2 = 1594 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333t + t2 = 1594 + 4.694444446 Combine like terms: 1594 + 4.694444446 = 1598.694444446 4.694444446 + -4.333333333t + t2 = 1598.694444446 Factor a perfect square on the left side: (t + -2.166666667)(t + -2.166666667) = 1598.694444446 Calculate the square root of the right side: 39.983677225 Break this problem into two subproblems by setting (t + -2.166666667) equal to 39.983677225 and -39.983677225.Subproblem 1
t + -2.166666667 = 39.983677225 Simplifying t + -2.166666667 = 39.983677225 Reorder the terms: -2.166666667 + t = 39.983677225 Solving -2.166666667 + t = 39.983677225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + t = 39.983677225 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + t = 39.983677225 + 2.166666667 t = 39.983677225 + 2.166666667 Combine like terms: 39.983677225 + 2.166666667 = 42.150343892 t = 42.150343892 Simplifying t = 42.150343892Subproblem 2
t + -2.166666667 = -39.983677225 Simplifying t + -2.166666667 = -39.983677225 Reorder the terms: -2.166666667 + t = -39.983677225 Solving -2.166666667 + t = -39.983677225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + t = -39.983677225 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + t = -39.983677225 + 2.166666667 t = -39.983677225 + 2.166666667 Combine like terms: -39.983677225 + 2.166666667 = -37.817010558 t = -37.817010558 Simplifying t = -37.817010558Solution
The solution to the problem is based on the solutions from the subproblems. t = {42.150343892, -37.817010558}
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