Solve the inequality and express your answer in interval notation x^2+12x+7< 0

(-11.385, -0.615)

Step-by-step explanation:

Inequation: x^2+12x+7<0

Equation: x^2+12x+7=0

Use the quadratic formula to get the roots of the equation.

Root 1:

-0.615

Root 2:

-11.385

Then, the inequality can be expressed as

(x + 0.615)*(x + 11.385)<0

There are 2 ways to satisfy it:  

x + 0.615 < 0 and x + 11.385 > 0

or

x + 0.615 > 0 and x + 11.385 < 0

For the first case:

x + 0.615 < 0 and x + 11.385 > 0

x < -0.615 and x > -11.385

In interval notation (-11.385, -0.615)

For the second case:

x + 0.615 > 0 and x + 11.385 < 0

x > -0.615 and x < -11.385

Which is impossible to satisfy. Therefore, the solution is (-11.385, -0.615)

what are the statements

step-by-step explanation: