Solve by Factoring x^2-5x+1=1

$x^{2} - 5 x + 1 = 1$

Step 1

Subtract $1$ from both sides of the equation.

$x^{2} - 5 x + 1 - 1 = 0$

Step 2

Combine the opposite terms in $x^{2} - 5 x + 1 - 1$ .

Subtract $1$ from $1$ .

$x^{2} - 5 x + 0 = 0$

Add $x^{2} - 5 x$ and $0$ .

$x^{2} - 5 x = 0$

Step 3

Factor $x$ out of $x^{2} - 5 x$ .

Factor $x$ out of $x^{2}$ .

$x \cdot x - 5 x = 0$

Factor $x$ out of $- 5 x$ .

$x \cdot x + x \cdot - 5 = 0$

Factor $x$ out of $x \cdot x + x \cdot - 5$ .

$x (x - 5) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 5 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Step 7

The final solution is all the values that make $x (x - 5) = 0$ true.

$x = 0, 5$