(x-2)^2=3x-8

To solve the equation (x-2)^2 = 3x - 8, we need to expand the left side and then simplify the equation.

First, let's expand (x-2)^2 using the formula for squaring a binomial: (x-2)^2 = x^2 - 4x + 4

Now, we substitute this back into the original equation: x^2 - 4x + 4 = 3x - 8

Next, we simplify the equation by moving all terms to one side: x^2 - 4x + 4 - 3x + 8 = 0 x^2 - 7x + 12 = 0

Finally, we can factorize this quadratic equation: (x - 3)(x - 4) = 0

Therefore, the solutions for the equation (x-2)^2 = 3x-8 are x = 3 and x = 4.

Таким образом, решениями уравнения (x-2)^2 = 3x-8 являются x = 3 и x = 4.