Question

use the quadratic formula to solve. express your answer in simplest form.

a² + 4a + 4 = 0

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 1\), \(b = 4\), \(c = 4\) (equation is \(a^2 + 4a + 4 = 0\), variable is \(a\)).

Step2: Quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Substitute \(a = 1\), \(b = 4\), \(c = 4\):
\(a=\frac{-4\pm\sqrt{4^2 - 4(1)(4)}}{2(1)}\)

Step3: Simplify discriminant

\(\sqrt{16 - 16}=\sqrt{0}=0\)

Step4: Solve for \(a\)

\(a=\frac{-4\pm0}{2}=\frac{-4}{2}=-2\) (double root)

Answer:

\(a = -2\) (with multiplicity 2)