Use the distributive property to multiply $x-4$ by $x+1$ and combine like terms.
$$x^{2}-3x-4=-4$$
Add $4$ to both sides.
$$x^{2}-3x-4+4=0$$
Add $-4$ and $4$ to get $0$.
$$x^{2}-3x=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $-3$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
Now solve the equation $x=\frac{3±3}{2}$ when $±$ is plus. Add $3$ to $3$.
$$x=\frac{6}{2}$$
Divide $6$ by $2$.
$$x=3$$
Now solve the equation $x=\frac{3±3}{2}$ when $±$ is minus. Subtract $3$ from $3$.
$$x=\frac{0}{2}$$
Divide $0$ by $2$.
$$x=0$$
The equation is now solved.
$$x=3$$ $$x=0$$
Steps for Completing the Square
Use the distributive property to multiply $x-4$ by $x+1$ and combine like terms.
$$x^{2}-3x-4=-4$$
Add $4$ to both sides.
$$x^{2}-3x=-4+4$$
Add $-4$ and $4$ to get $0$.
$$x^{2}-3x=0$$
Divide $-3$, the coefficient of the $x$ term, by $2$ to get $-\frac{3}{2}$. Then add the square of $-\frac{3}{2}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.
