SOLUTION: can you please help me solve this equation 12x^2 + 7 =10 ?

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Question 91863This question is from textbook
: can you please help me solve this equation 12x^2 + 7 =10 ? This question is from textbook

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
I'm assuming it looks like this right?

Subtract 10 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=12, b=7, and c=-10

Square 7 to get 49

Multiply to get

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

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 12 to get 24

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer