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erica [24]
3 years ago
14

Solve the inequality and express your answer in interval notation x^2+8x+5 <0

Mathematics
1 answer:
irakobra [83]3 years ago
7 0

The interval notation is (-\sqrt{11}-4, \sqrt{11}-4)

Explanation:

The inequality is x^{2}+8 x+5

Let us complete the square, we get,

x^{2}+8 x+5+4^{2}-4^{2}

Simplifying, we have,

(x+4)^{2}+5-4^{2}

(x+4)^{2}-11

Adding both sides of the equation by 11, we get,

(x+4)^{2}

Since, we know that for u^{n} , if n is even then -\sqrt[n]{a}

Thus, writing the above expression in this form, we get,

-\sqrt{11}

Also, if a then a and u

Then ,we have,

-\sqrt{11} and x+4

Solving the inequalities, we get,

-\sqrt{11}\ \ \ \ \ \  and  x+4

Merging the intervals, we have,

-\sqrt{11}-4

Hence, writing the solution in interval notation, we have,

(-\sqrt{11}-4, \sqrt{11}-4)

Therefore, the answer is (-\sqrt{11}-4, \sqrt{11}-4)

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