Question

question
use the quadratic formula to solve. express your answer in simplest form.
3x² + 20x + 25 = 0
answer attempt 1 out of 2
additional solution no solution
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Explanation:

Step1: Identify a, b, c values

For $3x^2 + 20x + 25 = 0$, $a=3$, $b=20$, $c=25$

Step2: Write quadratic formula

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Step3: Substitute values into formula

$$x = \frac{-20 \pm \sqrt{20^2 - 4(3)(25)}}{2(3)}$$

Step4: Calculate discriminant

$$\sqrt{400 - 300} = \sqrt{100} = 10$$

Step5: Simplify the expression

$$x = \frac{-20 \pm 10}{6}$$

Step6: Solve for both roots

First root: $x = \frac{-20 + 10}{6} = \frac{-10}{6} = -\frac{5}{3}$
Second root: $x = \frac{-20 - 10}{6} = \frac{-30}{6} = -5$

Answer:

$x = -5$ and $x = -\frac{5}{3}$