1 Answer

Lethargicpanda · Answer 1 · 2019-12-16T00:54:41+0000

The expression for the square of a binomial is

(a+b)^2 = a^2+2ab+b^2

Since your expression starts with
$x^2-6x +\ldots$

It means that
a = x , and so -6x must be twice the product of x and some number b. If you choose b = -3 you have

(x-3)^2 = x^2-6x+9

So, if you add 8 to both sides of your equation, you have

$x^2-6x+1+8 = 17+8 \iff x^2-6x+9 = 25 \iff (x-3)^2=25 \iff x-3 = \pm 5$

By choosing one sign at a time, we have the two solutions

$x_1 \to x-3 = 5 \iff x = 8$

$x_2 \to x-3 = -5 \iff x = -2$

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