Question

Write x2 − 2x + 25 = 0 in the form of (x − a)2 = b, where a and b are integers.

a (x − 2)2 = −24
b (x − 1)2 = −26
c (x − 2)2 = −25
d (x − 1)2 = −24

Answer 1

d (x − 1)^2 = −24

Explanation:

To write the equation x^2 - 2x + 25 = 0 in the form of (x - a)^2 = b, where a and b are integers, we need to complete the square.

First, let's complete the square on the left side of the equation:

x^2 - 2x + 25 = 0

To complete the square, we need to add and subtract the square of half the coefficient of x. In this case, the coefficient of x is -2, so we have:

x^2 - 2x + (-2/2)^2 = -25 + (-2/2)^2

Simplifying:

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

x^2 - 2x + 1 = -24

Now, we can rewrite the left side of the equation as a perfect square:

(x - 1)^2 = -24

So, the equation x^2 - 2x + 25 = 0 can be written in the form (x - a)^2 = b as:

d (x - 1)^2 = -24

Hope this helps!