Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+4\right)^{2}$.
$$x^{2}+8x+16=9$$
Subtract $9$ from both sides.
$$x^{2}+8x+16-9=0$$
Subtract $9$ from $16$ to get $7$.
$$x^{2}+8x+7=0$$
To solve the equation, factor $x^{2}+8x+7$ using formula $x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right)$. To find $a$ and $b$, set up a system to be solved.
$$a+b=8$$ $$ab=7$$
Since $ab$ is positive, $a$ and $b$ have the same sign. Since $a+b$ is positive, $a$ and $b$ are both positive. The only such pair is the system solution.
$$a=1$$ $$b=7$$
Rewrite factored expression $\left(x+a\right)\left(x+b\right)$ using the obtained values.
$$\left(x+1\right)\left(x+7\right)$$
To find equation solutions, solve $x+1=0$ and $x+7=0$.
$$x=-1$$ $$x=-7$$
Steps Using Factoring By Grouping
Divide both sides by $2$.
$$\left(x+4\right)^{2}=\frac{18}{2}$$
Divide $18$ by $2$ to get $9$.
$$\left(x+4\right)^{2}=9$$
Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+4\right)^{2}$.
$$x^{2}+8x+16=9$$
Subtract $9$ from both sides.
$$x^{2}+8x+16-9=0$$
Subtract $9$ from $16$ to get $7$.
$$x^{2}+8x+7=0$$
To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as $x^{2}+ax+bx+7$. To find $a$ and $b$, set up a system to be solved.
$$a+b=8$$ $$ab=1\times 7=7$$
Since $ab$ is positive, $a$ and $b$ have the same sign. Since $a+b$ is positive, $a$ and $b$ are both positive. The only such pair is the system solution.
$$a=1$$ $$b=7$$
Rewrite $x^{2}+8x+7$ as $\left(x^{2}+x\right)+\left(7x+7\right)$.
$$\left(x^{2}+x\right)+\left(7x+7\right)$$
Factor out $x$ in the first and $7$ in the second group.
$$x\left(x+1\right)+7\left(x+1\right)$$
Factor out common term $x+1$ by using distributive property.
$$\left(x+1\right)\left(x+7\right)$$
To find equation solutions, solve $x+1=0$ and $x+7=0$.
$$x=-1$$ $$x=-7$$
Steps Using the Quadratic Formula
Divide both sides by $2$.
$$\left(x+4\right)^{2}=\frac{18}{2}$$
Divide $18$ by $2$ to get $9$.
$$\left(x+4\right)^{2}=9$$
Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+4\right)^{2}$.
$$x^{2}+8x+16=9$$
Subtract $9$ from both sides.
$$x^{2}+8x+16-9=0$$
Subtract $9$ from $16$ to get $7$.
$$x^{2}+8x+7=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $8$ for $b$, and $7$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{-8±\sqrt{8^{2}-4\times 7}}{2}$$
Square $8$.
$$x=\frac{-8±\sqrt{64-4\times 7}}{2}$$
Multiply $-4$ times $7$.
$$x=\frac{-8±\sqrt{64-28}}{2}$$
Add $64$ to $-28$.
$$x=\frac{-8±\sqrt{36}}{2}$$
Take the square root of $36$.
$$x=\frac{-8±6}{2}$$
Now solve the equation $x=\frac{-8±6}{2}$ when $±$ is plus. Add $-8$ to $6$.
$$x=-\frac{2}{2}$$
Divide $-2$ by $2$.
$$x=-1$$
Now solve the equation $x=\frac{-8±6}{2}$ when $±$ is minus. Subtract $6$ from $-8$.
$$x=-\frac{14}{2}$$
Divide $-14$ by $2$.
$$x=-7$$
The equation is now solved.
$$x=-1$$ $$x=-7$$
Steps for Completing the Square
Divide both sides by $2$.
$$\left(x+4\right)^{2}=\frac{18}{2}$$
Divide $18$ by $2$ to get $9$.
$$\left(x+4\right)^{2}=9$$
Take the square root of both sides of the equation.
