Question

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

Answer 1

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