To solve the quadratic equation \(4x^2 + 12x + 9 = 0\) by factoring using the perfect square trinomial pattern, we first recognize that the equation can be expressed in the form \((ax + b)^2 = 0\).
-
Start by rewriting the equation:
\[ 4x^2 + 12x + 9 = 0 \]
-
Identify the coefficients:
- The coefficient of \(x^2\) is \(4\), which is \( (2x)^2 \).
- The constant term is \(9\), which is \(3^2\).
- The middle term \(12x\) can be expressed as \(2 \times 2x \times 3\).
-
Since the quadratic can be formed as a perfect square, we can rewrite it as:
\[ (2x + 3)^2 = 0 \]
-
Setting the factored form equal to zero:
\[ (2x + 3)^2 = 0 \]
-
Solve for \(x\):
\[ 2x + 3 = 0 \] \[ 2x = -3 \] \[ x = -\frac{3}{2} \]
Thus, the solution to the equation \(4x^2 + 12x + 9 = 0\) is:
\[ \boxed{-\frac{3}{2}} \]
1 answer