Use the distributive property to multiply $X+5$ by $X-3$ and combine like terms.
$$X^{2}+2X-15-X=5$$
Combine $2X$ and $-X$ to get $X$.
$$X^{2}+X-15=5$$
Subtract $5$ from both sides.
$$X^{2}+X-15-5=0$$
Subtract $5$ from $-15$ to get $-20$.
$$X^{2}+X-20=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $1$ for $b$, and $-20$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$X=\frac{-1±\sqrt{1^{2}-4\left(-20\right)}}{2}$$
Square $1$.
$$X=\frac{-1±\sqrt{1-4\left(-20\right)}}{2}$$
Multiply $-4$ times $-20$.
$$X=\frac{-1±\sqrt{1+80}}{2}$$
Add $1$ to $80$.
$$X=\frac{-1±\sqrt{81}}{2}$$
Take the square root of $81$.
$$X=\frac{-1±9}{2}$$
Now solve the equation $X=\frac{-1±9}{2}$ when $±$ is plus. Add $-1$ to $9$.
$$X=\frac{8}{2}$$
Divide $8$ by $2$.
$$X=4$$
Now solve the equation $X=\frac{-1±9}{2}$ when $±$ is minus. Subtract $9$ from $-1$.
$$X=-\frac{10}{2}$$
Divide $-10$ by $2$.
$$X=-5$$
The equation is now solved.
$$X=4$$ $$X=-5$$
Steps for Completing the Square
Use the distributive property to multiply $X+5$ by $X-3$ and combine like terms.
$$X^{2}+2X-15-X=5$$
Combine $2X$ and $-X$ to get $X$.
$$X^{2}+X-15=5$$
Add $15$ to both sides.
$$X^{2}+X=5+15$$
Add $5$ and $15$ to get $20$.
$$X^{2}+X=20$$
Divide $1$, the coefficient of the $x$ term, by $2$ to get $\frac{1}{2}$. Then add the square of $\frac{1}{2}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.
