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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.

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step-by-step explanation: