Question

Solve √(25-x^2)=x-1 by factorization method

Answer 1

square both sides of the equation

25 - x^2 = (x-1)^2

25 -x^2 = x^2 -2x+1

0 = 2x^2 -2x +1-25

2x^2 -2x -24 =0

x^2 -x -12 =0 [ dividing each term with 2]

x^2 -4x +3x -12=0

x(x-4)+3(x-4)=0

(x-4)(x+3)=0
therefore

x-4 =0  or x+3 =0

x= 4 or x= -3