solve the equation x^2 -5x +1 = 25

We can see from the term x^2 that this equation is quadratic. To solve it, we need to get it into the form ax^2 +bx +c = 0. Subtract 25 from both sides to reach this form:So we have the equation x^2 -5x - 24 = 0
The simplest way to solve quadratic equations is by factorising them into two sets of brackets (e.g. in the form (x + a)(x - b)). In this case, the two numbers need to multiply to give '-24'.The two numbers need to add to give '-5'.
One such pair of numbers is '3' and '-8'.This means the factorised equation will be (x+3)(x-8) = 0
From here, we can look at the equation and see that if we make x = -3 or x = 8 then one of the brackets will be equal to zero, meaning the entire term will be equal to zero (which is the right hand side of the equation).
So the solutions are x = -3, x= 8