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

User Dusk
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1 Answer

3 votes

The interval notation is
(-√(11)-4, √(11)-4)

Step-by-step explanation:

The inequality is
x^(2)+8 x+5<0

Let us complete the square, we get,


x^(2)+8 x+5+4^(2)-4^(2)<0

Simplifying, we have,


(x+4)^(2)+5-4^(2)<0


(x+4)^(2)-11<0

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


(x+4)^(2)<11

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

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


-√(11)<x+4<√(11)

Also, if
a<u<b then
a<u and
u<b

Then ,we have,


-√(11)<x+4 and
x+4<√(11)

Solving the inequalities, we get,


-√(11)\ \ \ \ \ \ <x+4\\-√(11)-4<x and
x+4<√(11)\\x \ \ \ \ \ <√(11)-4

Merging the intervals, we have,


-√(11)-4<x<√(11)-4

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


(-√(11)-4, √(11)-4)

Therefore, the answer is
(-√(11)-4, √(11)-4)

User Tomas Pruzina
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6.7k points