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Simplifying 16t2 + -22t + -7 = 0 Reorder the terms: -7 + -22t + 16t2 = 0 Solving -7 + -22t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + -1.375t + t2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -1.375t + 0.4375 + t2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -1.375t + t2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -1.375t + t2 = 0 + 0.4375 -1.375t + t2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -1.375t + t2 = 0.4375 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 = 0.4375 + 0.47265625 Reorder the terms: 0.47265625 + -1.375t + t2 = 0.4375 + 0.47265625 Combine like terms: 0.4375 + 0.47265625 = 0.91015625 0.47265625 + -1.375t + t2 = 0.91015625 Factor a perfect square on the left side: (t + -0.6875)(t + -0.6875) = 0.91015625 Calculate the square root of the right side: 0.954021095 Break this problem into two subproblems by setting (t + -0.6875) equal to 0.954021095 and -0.954021095.Subproblem 1
t + -0.6875 = 0.954021095 Simplifying t + -0.6875 = 0.954021095 Reorder the terms: -0.6875 + t = 0.954021095 Solving -0.6875 + t = 0.954021095 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 = 0.954021095 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + t = 0.954021095 + 0.6875 t = 0.954021095 + 0.6875 Combine like terms: 0.954021095 + 0.6875 = 1.641521095 t = 1.641521095 Simplifying t = 1.641521095Subproblem 2
t + -0.6875 = -0.954021095 Simplifying t + -0.6875 = -0.954021095 Reorder the terms: -0.6875 + t = -0.954021095 Solving -0.6875 + t = -0.954021095 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 = -0.954021095 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + t = -0.954021095 + 0.6875 t = -0.954021095 + 0.6875 Combine like terms: -0.954021095 + 0.6875 = -0.266521095 t = -0.266521095 Simplifying t = -0.266521095Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.641521095, -0.266521095}
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