Answer:
x = 16 or x = 26
Step-by-step explanation:
(x – 21)² = 25
Expand
(x – 21)(x – 21) = 25
x² – 21x – 21x + 441 = 25
x² – 21x – 21x + 441 – 25 = 0
x² – 42x + 416 = 0
We shall solve by Factorisation method as shown below:
x² – 42x + 416 = 0
Multiply the first term, x² and the last term, 416 together. The result is 416x².
Find two factors of 416x² such that the sum of the factors will result to the 2nd term, – 42x in the expression above.
The factors are – 26x and – 16x.
Now, replace the 2nd term, – 42x with – 26x and – 16x. This is illustrated below:
x² – 42x + 416 = 0
x² – 26x – 16x + 416 = 0
Factorise
x(x – 26) – 16(x – 26) = 0
(x – 16)(x – 26) = 0
x – 16 = 0 or x – 26 = 0
x = 16 or x = 26
Therefore, the solutions to the equation (x – 21)² = 25 are 16 and 26.
