Question

Solve the following quadratic equation by factoring using the perfect square trinomial pattern: 4x2+12x+9=0.(1 point)

Answer 1

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 \((ax + b)^2 = 0\).

1. Start by rewriting the equation:

\[
4x^2 + 12x + 9 = 0
\]

2. 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 \(2 \times 2x \times 3\).

3. Since the quadratic can be formed as a perfect square, we can rewrite it as:

\[
(2x + 3)^2 = 0
\]

4. Setting the factored form equal to zero:

\[
(2x + 3)^2 = 0
\]

5. Solve for \(x\):

\[
2x + 3 = 0
\]
\[
2x = -3
\]
\[
x = -\frac{3}{2}
\]

Thus, the solution to the equation \(4x^2 + 12x + 9 = 0\) is:

\[
\boxed{-\frac{3}{2}}
\]