Question

Solve the equation after making an appropriate substitution.

[ (11x - 1)² - 3(11x - 1) - 4 = 0 ]

Determine the appropriate substitution using the new variable ( u ):

[ u = ]

Answer 1

To solve the equation (11x - 1)² - 3(11x - 1) - 4 = 0, make the substitution u = 11x - 1. Solve the resulting quadratic equation u² - 3u - 4 = 0 using factoring or the quadratic formula. Substitute back in the original expression for u to find the values of x.

Step-by-step explanation:

To solve the equation (11x - 1)² - 3(11x - 1) - 4 = 0, we can make the substitution u = 11x - 1. This will simplify the equation and make it easier to solve. Now we have u² - 3u - 4 = 0. We can solve this quadratic equation using factoring or the quadratic formula.

Using factoring, we can rewrite the equation as (u - 4)(u + 1) = 0. Setting each factor equal to zero, we find u = 4 or u = -1. Now we can substitute back in the original expression for u to find the values of x. For u = 4, we have 11x - 1 = 4, which gives x = 5/11. For u = -1, we have 11x - 1 = -1, which gives x = 0.