10. Quadratic Equations

A quadratic equation has an \(x^2\) term. Many GED®-level quadratics can be solved by factoring or square roots.

Example 1:
\[ x^2=49. \]
Take the square root of both sides:
\[ x=7 \quad \text{or} \quad x=-7. \]

Example 2:
\[ x^2-9=0. \]
Add 9:
\[ x^2=9. \]
So:
\[ x=3 \quad \text{or} \quad x=-3. \]

Example 3:
\[ x^2+5x+6=0. \]
Factor:
\[ (x+2)(x+3)=0. \]
Set each factor equal to zero:
\[ x=-2 \quad \text{or} \quad x=-3. \]

Example 4:
\[ x^2=5x. \]
Move all terms to one side:
\[ x^2-5x=0. \]
Factor:
\[ x(x-5)=0. \]
So:
\[ x=0 \quad \text{or} \quad x=5. \]

Common mistake: dividing both sides by \(x\) in \(x^2=5x\). That loses the solution \(x=0\). Move all terms to one side and factor.