SOLUTION: 24x�-2x=15 solve the equation by factoring and quadratic formula

Question 102791: 24x�-2x=15 solve the equation by factoring and quadratic formula
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"24x�-2x=15 solve the equation by factoring"

Start with the given equation

Subtract 15 from both sides

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:

or

or Now solve for x in each case

So our solutions are

or

Notice if we graph we get

and we can see that the graph has roots at and , so this verifies our answer.

"4x�-2x=15 solve the equation by the quadratic formula"

Start with the given equation

Subtract 15 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=24, b=-2, and c=-15

Negate -2 to get 2

Square -2 to get 4 (note: remember when you square -2, 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 24 to get 48

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

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