SOLUTION: Can you help with this problem? It's a take home exercise that has me stumped: Solve: 2x2 (2x squared) = 7x + 11 I incorrectly listed this under "Word Problems." Thank you.

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Question 110771: Can you help with this problem? It's a take home exercise that has me stumped:
Solve: 2x2 (2x squared) = 7x + 11
I incorrectly listed this under "Word Problems." Thank you.

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given equation

Subtract from both sides

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-2, b=7, and c=11

Square 7 to get 49

Multiply to get

Combine like terms in the radicand (everything under the square root)

Multiply 2 and -2 to get -4

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our solutions are:
or

Notice when we graph , we get:

when we use the root finder feature on a calculator, we find that and .So this verifies our answer