Use the distributive property to multiply $x-1$ by $x+3$ and combine like terms.
$$x^{2}+2x-3=12$$
Subtract $12$ from both sides.
$$x^{2}+2x-3-12=0$$
Subtract $12$ from $-3$ to get $-15$.
$$x^{2}+2x-15=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $2$ for $b$, and $-15$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{-2±\sqrt{2^{2}-4\left(-15\right)}}{2}$$
Square $2$.
$$x=\frac{-2±\sqrt{4-4\left(-15\right)}}{2}$$
Multiply $-4$ times $-15$.
$$x=\frac{-2±\sqrt{4+60}}{2}$$
Add $4$ to $60$.
$$x=\frac{-2±\sqrt{64}}{2}$$
Take the square root of $64$.
$$x=\frac{-2±8}{2}$$
Now solve the equation $x=\frac{-2±8}{2}$ when $±$ is plus. Add $-2$ to $8$.
$$x=\frac{6}{2}$$
Divide $6$ by $2$.
$$x=3$$
Now solve the equation $x=\frac{-2±8}{2}$ when $±$ is minus. Subtract $8$ from $-2$.
$$x=-\frac{10}{2}$$
Divide $-10$ by $2$.
$$x=-5$$
The equation is now solved.
$$x=3$$ $$x=-5$$
Steps for Completing the Square
Use the distributive property to multiply $x-1$ by $x+3$ and combine like terms.
$$x^{2}+2x-3=12$$
Add $3$ to both sides.
$$x^{2}+2x=12+3$$
Add $12$ and $3$ to get $15$.
$$x^{2}+2x=15$$
Divide $2$, the coefficient of the $x$ term, by $2$ to get $1$. Then add the square of $1$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.
$$x^{2}+2x+1^{2}=15+1^{2}$$
Square $1$.
$$x^{2}+2x+1=15+1$$
Add $15$ to $1$.
$$x^{2}+2x+1=16$$
Factor $x^{2}+2x+1$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.
$$\left(x+1\right)^{2}=16$$
Take the square root of both sides of the equation.
