# How do you solve #1/2x^2+3x<=-6# by algebraically?

##### 2 Answers

The solution is

#### Explanation:

Let's rewrite the inequality

Let

To calculate the roots of

As,

So,

graph{1/2x^2+3x+6 [-18.7, 13.34, -2.56, 13.46]}

No value for

#### Explanation:

Given

Note that you can multiply both sides of an inequality by any positive value and still maintain the validity and orientation of the inequality.

Multiplying both sides by

Note [2] we can add any amount to both sides of an inequality without effecting the validity or orientation of the inequality.

Adding

Note [3] since

Rewriting

with vertex at

Evaluating

we find

Since this value is greater than

no value exists for