Completing the square on $4x^2+12x+5=0$ gives $(2x+3{)}^2=q$. Find $q$.

Rewrite $a{x}^2+bx+c$ into the form $a(x-h{)}^2+k$.

**Steps for $x^2+bx+c=0$**:
1. Take half the coefficient of $x:b/2$.
2. Square it: $(b/2{)}^2$.
3. Add and subtract this value to complete the perfect square.

Example: $x^2+6x+5=0$.
→ $(x^2+6x+9)-9+5=0$
→ $(x+3{)}^2=4$
→ $x+3=$ ±2 → $x=-1$ or −5.

Completing the square is how the quadratic formula is DERIVED. It's slower than factorisation but works ALWAYS (no clever guessing required).