How do you solve x(x-5) plus x^2 = 3?

Question

and (x-2)(x-5) = 1?

is there a solution? :) thanks a lot!

Answer 1

x(x-5) + x^2 =3

x^2 - 5x + x^2 =3

2x^2 - 5x - 3 = 0

using cross method

(2x + 1)(x - 3) = 0

2x + 1 = 0 or x - 3 = 0

x = -1/2 or x = 3

(x - 2)(x - 5) = 1       (expand LHS)

x^2 - 5x - 2x +10 = 1

x^2 - 7x + 9 = 0

you cant really use cross method, so use the quadratic formula to solve for x. there should be 2 solutions.

Answer 2

Of course there is a solution and you solve it by applying the basic rules of algebra.