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Simplifying -16t2 + 22t + 22 = 0 Reorder the terms: 22 + 22t + -16t2 = 0 Solving 22 + 22t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + 11t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 11t + -8t2)' equal to zero and attempt to solve: Simplifying 11 + 11t + -8t2 = 0 Solving 11 + 11t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.375 + -1.375t + t2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + -1.375t + 1.375 + t2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + -1.375t + t2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + -1.375t + t2 = 0 + 1.375 -1.375t + t2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 -1.375t + t2 = 1.375 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 = 1.375 + 0.47265625 Reorder the terms: 0.47265625 + -1.375t + t2 = 1.375 + 0.47265625 Combine like terms: 1.375 + 0.47265625 = 1.84765625 0.47265625 + -1.375t + t2 = 1.84765625 Factor a perfect square on the left side: (t + -0.6875)(t + -0.6875) = 1.84765625 Calculate the square root of the right side: 1.359285198 Break this problem into two subproblems by setting (t + -0.6875) equal to 1.359285198 and -1.359285198.Subproblem 1
t + -0.6875 = 1.359285198 Simplifying t + -0.6875 = 1.359285198 Reorder the terms: -0.6875 + t = 1.359285198 Solving -0.6875 + t = 1.359285198 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 = 1.359285198 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + t = 1.359285198 + 0.6875 t = 1.359285198 + 0.6875 Combine like terms: 1.359285198 + 0.6875 = 2.046785198 t = 2.046785198 Simplifying t = 2.046785198Subproblem 2
t + -0.6875 = -1.359285198 Simplifying t + -0.6875 = -1.359285198 Reorder the terms: -0.6875 + t = -1.359285198 Solving -0.6875 + t = -1.359285198 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 = -1.359285198 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + t = -1.359285198 + 0.6875 t = -1.359285198 + 0.6875 Combine like terms: -1.359285198 + 0.6875 = -0.671785198 t = -0.671785198 Simplifying t = -0.671785198Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.046785198, -0.671785198}Solution
t = {2.046785198, -0.671785198}
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