Solve the equation: (60)/(x-5) - (6)/(x) = (1)/(6)

Hey She🦋is🎀Rodiah, good to see you again. Step 1: Combine the fractions on the left side of the equation. The given equation is: (60)/(x-5) - (6)/(x) = (1)/(6) Find a common denominator for the left side, which is x(x-5): (60x - 6(x-5))/(x(x-5)) = (1)/(6) Distribute the -6: (60x - 6x + 30)/(x^2 - 5x) = (1)/(6) Combine like terms in the numerator: (54x + 30)/(x^2 - 5x) = (1)/(6) Step 2: Eliminate denominators by cross-multiplication. Multiply both sides by 6(x^2 - 5x): 6(54x + 30) = 1(x^2 - 5x) Distribute the 6 on the left side: 324x + 180 = x^2 - 5x Step 3: Rearrange the equation into the standard quadratic form ax^2 + bx + c = 0. Move all terms to the right side to set the equation to zero: 0 = x^2 - 5x - 324x - 180 Combine like terms: x^2 - 329x - 180 = 0 Step 4: Apply the completing the square method to solve for x. Move the constant term to the right side: x^2 - 329x = 180 To complete the square, add ((b)/(2))^2 to both sides. Here, b = -329. So, ((-329)/(2))^2 = (108241)/(4). x^2 - 329x + ((-329)/(2))^2 = 180 + ((-329)/(2))^2 (x - (329)/(2))^2 = 180 + (108241)/(4) Convert 180 to a fraction with denominator 4: 180 = (180 × 4)/(4) = (720)/(4). (x - (329)/(2))^2 = (720)/(4) + (108241)/(4) (x - (329)/(2))^2 = (720 + 108241)/(4) (x - (329)/(2))^2 = (108961)/(4) Take the square root of both sides: x - (329)/(2) = ±sqrt((108961)/(4)) x - (329)/(2) = ±sqrt(108961)sqrt(4) x - (329)/(2) = ±sqrt(108961)2 Solve for x: x = (329)/(2) ± sqrt(108961)2 x = 329 ± sqrt(108961)2 The two solutions are: x_1 = 329 + sqrt(108961)2 x_2 = 329 - sqrt(108961)2 The final answers are x = 329 ± sqrt(108961)2. Send me the next one 📸