This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To solve the equation (8t - 2)/(5) = (2)/(t), we will cross-multiply and then solve the resulting quadratic equation. Step 1: Cross-multiply the terms. t(8t - 2) = 5(2) 8t^2 - 2t = 10 Step 2: Rearrange the equation into the standard quadratic form at^2 + bt + c = 0. 8t^2 - 2t - 10 = 0 Divide the entire equation by 2 to simplify the coefficients: 4t^2 - t - 5 = 0 Step 3: Solve the quadratic equation using the quadratic formula t = -b ± sqrt(b^2 - 4ac)2a. For 4t^2 - t - 5 = 0, we have a = 4, b = -1, and c = -5. t = -(-1) ± sqrt((-1)^2 - 4(4)(-5))2(4) t = 1 ± sqrt(1 - (-80))8 t = 1 ± sqrt(1 + 80)8 t = 1 ± sqrt(81)8 t = (1 ± 9)/(8) Step 4: Calculate the two possible values for t. t_1 = (1 + 9)/(8) = (10)/(8) = (5)/(4) t_2 = (1 - 9)/(8) = (-8)/(8) = -1 The solutions for t are (5)/(4) and -1. t = (5)/(4), -1 Drop the next question 📸