SOLUTION: Prove that if {{{3x^2+6=18}}} and x<0, then x=-2 is true.

Question 188693: Prove that if and x<0, then x=-2 is true.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Subtract 18 from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the answers are or

However, since , this means that "x" is negative. So this means that is the only solution (if the inequality restriction is applied).
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