SOLUTION: solve 4w^2=10w-4

Question 96217: solve
4w^2=10w-4
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Get all terms to one side

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

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=4, b=-10, and c=4

Negate -10 to get 10

Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because .)

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 4 to get 8

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 (just replace w with x), we get:

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