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Simplifying -16t2 + 288t + 216 = 0 Reorder the terms: 216 + 288t + -16t2 = 0 Solving 216 + 288t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(27 + 36t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(27 + 36t + -2t2)' equal to zero and attempt to solve: Simplifying 27 + 36t + -2t2 = 0 Solving 27 + 36t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -13.5 + -18t + t2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -18t + 13.5 + t2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -18t + t2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -18t + t2 = 0 + 13.5 -18t + t2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -18t + t2 = 13.5 The t term is -18t. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18t + 81 + t2 = 13.5 + 81 Reorder the terms: 81 + -18t + t2 = 13.5 + 81 Combine like terms: 13.5 + 81 = 94.5 81 + -18t + t2 = 94.5 Factor a perfect square on the left side: (t + -9)(t + -9) = 94.5 Calculate the square root of the right side: 9.721111048 Break this problem into two subproblems by setting (t + -9) equal to 9.721111048 and -9.721111048.Subproblem 1
t + -9 = 9.721111048 Simplifying t + -9 = 9.721111048 Reorder the terms: -9 + t = 9.721111048 Solving -9 + t = 9.721111048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 9.721111048 + 9 Combine like terms: -9 + 9 = 0 0 + t = 9.721111048 + 9 t = 9.721111048 + 9 Combine like terms: 9.721111048 + 9 = 18.721111048 t = 18.721111048 Simplifying t = 18.721111048Subproblem 2
t + -9 = -9.721111048 Simplifying t + -9 = -9.721111048 Reorder the terms: -9 + t = -9.721111048 Solving -9 + t = -9.721111048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = -9.721111048 + 9 Combine like terms: -9 + 9 = 0 0 + t = -9.721111048 + 9 t = -9.721111048 + 9 Combine like terms: -9.721111048 + 9 = -0.721111048 t = -0.721111048 Simplifying t = -0.721111048Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.721111048, -0.721111048}Solution
t = {18.721111048, -0.721111048}
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