Question - Solving a Quadratic Equation Using the Quadratic Formula
Solution:
To solve the quadratic equation $$ a^2 + 4a + 4 = 0 $$ using the quadratic formula, we need to identify the coefficients of the equation, which are in the standard form $$ ax^2 + bx + c = 0 $$.For this equation:$$ a = 1 $$$$ b = 4 $$$$ c = 4 $$The quadratic formula is given by:\[ x = \frac{{-b \pm \sqrt{b^2 - 4ac}}}{{2a}} \]Plugging in the coefficients:\[ x = \frac{{-4 \pm \sqrt{4^2 - 4 \cdot 1 \cdot 4}}}{{2 \cdot 1}} \]\[ x = \frac{{-4 \pm \sqrt{16 - 16}}}{{2}} \]\[ x = \frac{{-4 \pm \sqrt{0}}}{{2}} \]\[ x = \frac{{-4 \pm 0}}{{2}} \]\[ x = \frac{{-4}}{{2}} \]\[ x = -2 \]Since the discriminant ($$ b^2 - 4ac $$) is zero, there is one real, repeated solution to the equation. Therefore, the solution to the equation $$ a^2 + 4a + 4 = 0 $$ is $$ x = -2 $$. This is the simplest form.
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