Question

Solve the equation below by completing the square and then solving for x. X2 - 6x + 1 = 17

Answer 1

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

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

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