Use the distributive property to multiply $x-10$ by $x+20$ and combine like terms.
$$x^{2}+10x-200=1000$$
Subtract $1000$ from both sides.
$$x^{2}+10x-200-1000=0$$
Subtract $1000$ from $-200$ to get $-1200$.
$$x^{2}+10x-1200=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $10$ for $b$, and $-1200$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
Now solve the equation $x=\frac{-10±70}{2}$ when $±$ is plus. Add $-10$ to $70$.
$$x=\frac{60}{2}$$
Divide $60$ by $2$.
$$x=30$$
Now solve the equation $x=\frac{-10±70}{2}$ when $±$ is minus. Subtract $70$ from $-10$.
$$x=-\frac{80}{2}$$
Divide $-80$ by $2$.
$$x=-40$$
The equation is now solved.
$$x=30$$ $$x=-40$$
Steps for Completing the Square
Use the distributive property to multiply $x-10$ by $x+20$ and combine like terms.
$$x^{2}+10x-200=1000$$
Add $200$ to both sides.
$$x^{2}+10x=1000+200$$
Add $1000$ and $200$ to get $1200$.
$$x^{2}+10x=1200$$
Divide $10$, the coefficient of the $x$ term, by $2$ to get $5$. Then add the square of $5$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.
$$x^{2}+10x+5^{2}=1200+5^{2}$$
Square $5$.
$$x^{2}+10x+25=1200+25$$
Add $1200$ to $25$.
$$x^{2}+10x+25=1225$$
Factor $x^{2}+10x+25$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.
$$\left(x+5\right)^{2}=1225$$
Take the square root of both sides of the equation.
