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Simplifying -16t2 + 22t + 330 = 0 Reorder the terms: 330 + 22t + -16t2 = 0 Solving 330 + 22t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(165 + 11t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(165 + 11t + -8t2)' equal to zero and attempt to solve: Simplifying 165 + 11t + -8t2 = 0 Solving 165 + 11t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -20.625 + -1.375t + t2 = 0 Move the constant term to the right: Add '20.625' to each side of the equation. -20.625 + -1.375t + 20.625 + t2 = 0 + 20.625 Reorder the terms: -20.625 + 20.625 + -1.375t + t2 = 0 + 20.625 Combine like terms: -20.625 + 20.625 = 0.000 0.000 + -1.375t + t2 = 0 + 20.625 -1.375t + t2 = 0 + 20.625 Combine like terms: 0 + 20.625 = 20.625 -1.375t + t2 = 20.625 The t term is -1.375t. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375t + 0.47265625 + t2 = 20.625 + 0.47265625 Reorder the terms: 0.47265625 + -1.375t + t2 = 20.625 + 0.47265625 Combine like terms: 20.625 + 0.47265625 = 21.09765625 0.47265625 + -1.375t + t2 = 21.09765625 Factor a perfect square on the left side: (t + -0.6875)(t + -0.6875) = 21.09765625 Calculate the square root of the right side: 4.593218507 Break this problem into two subproblems by setting (t + -0.6875) equal to 4.593218507 and -4.593218507.Subproblem 1
t + -0.6875 = 4.593218507 Simplifying t + -0.6875 = 4.593218507 Reorder the terms: -0.6875 + t = 4.593218507 Solving -0.6875 + t = 4.593218507 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + t = 4.593218507 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + t = 4.593218507 + 0.6875 t = 4.593218507 + 0.6875 Combine like terms: 4.593218507 + 0.6875 = 5.280718507 t = 5.280718507 Simplifying t = 5.280718507Subproblem 2
t + -0.6875 = -4.593218507 Simplifying t + -0.6875 = -4.593218507 Reorder the terms: -0.6875 + t = -4.593218507 Solving -0.6875 + t = -4.593218507 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + t = -4.593218507 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + t = -4.593218507 + 0.6875 t = -4.593218507 + 0.6875 Combine like terms: -4.593218507 + 0.6875 = -3.905718507 t = -3.905718507 Simplifying t = -3.905718507Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.280718507, -3.905718507}Solution
t = {5.280718507, -3.905718507}
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