Solve for x 1=x^2-6x+9

$1 = x^{2} - 6 x + 9$

Step 1

Rewrite the equation as $x^{2} - 6 x + 9 = 1$ .

$x^{2} - 6 x + 9 = 1$

Step 2

Subtract $1$ from both sides of the equation.

$x^{2} - 6 x + 9 - 1 = 0$

Step 3

Subtract $1$ from $9$ .

$x^{2} - 6 x + 8 = 0$

Step 4

Factor $x^{2} - 6 x + 8$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $8$ and whose sum is $- 6$ .

$- 4, - 2$

Write the factored form using these integers.

$(x - 4) (x - 2) = 0$

Step 5

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

$x - 4 = 0$

$x - 2 = 0$

Step 6

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 7

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Step 8

The final solution is all the values that make $(x - 4) (x - 2) = 0$ true.

$x = 4, 2$

Solve for x 1=x^2-6x+9

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