Solve by Factoring x^2-17=-1

$x^{2} - 17 = - 1$

Step 1

Add $1$ to both sides of the equation.

$x^{2} - 17 + 1 = 0$

Step 2

Add $- 17$ and $1$ .

$x^{2} - 16 = 0$

Step 3

Rewrite $16$ as $4^{2}$ .

$x^{2} - 4^{2} = 0$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 4$ .

$(x + 4) (x - 4) = 0$

Step 5

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

$x + 4 = 0$

$x - 4 = 0$

Step 6

Set $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 7

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Step 8

The final solution is all the values that make $(x + 4) (x - 4) = 0$ true.

$x = - 4, 4$