Solve Using the Square Root Property x^2+6x+9=1

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

Step 1

Subtract $1$ from both sides of the equation.

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

Step 2

Subtract $1$ from $9$ .

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

Step 3

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 $6$ .

$2, 4$

Write the factored form using these integers.

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

Step 4

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

$x + 2 = 0$

$x + 4 = 0$

Step 5

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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

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

$x = - 2, - 4$

Solve Using the Square Root Property x^2+6x+9=1

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