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Solve for x. Round your answer to the nearest hundredth.

\[ x^2 + 6x + 3 = 0 \]

A. \( x = -5.45 \) or \( x = -0.55 \)
B. \( x = -6.46 \) or \( x = 0.46 \)
C. \( x = 1.37 \) or \( x = -0.22 \)
D. No real solutions

Answer :

Final answer:

To solve for x in the equation x² + 6x + 3 = 0, we can use the quadratic formula. The solutions to the equation, rounded to the nearest hundredth, are x ≈ -5.45 and x ≈ -0.55.


Explanation:

To solve the equation x² + 6x + 3 = 0, we can use the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions are given by:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 1, b = 6, and c = 3. Plugging in these values into the quadratic formula, we get:

x = (-6 ± √(6² - 4(1)(3))) / (2(1))

Simplifying further, we have:

x = (-6 ± √(36 - 12)) / 2

x = (-6 ± √24) / 2

x = (-6 ± 2√6) / 2

x = -3 ± √6

Therefore, the approximate solutions to the equation x² + 6x + 3 = 0, rounded to the nearest hundredth, are x ≈ -3 - √6 and x ≈ -3 + √6, which can be simplified as:

x ≈ -5.45

x ≈ -0.55

So the correct answer is option A: x = -5.45 or x = -0.55.


Learn more about Quadratic equations here:

https://brainly.com/question/34196754


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