SOLUTION: Solve {{{4x^2=12}}} Find the x-intercepts of {{{f(x)=4x^2-12}}}

Question 130760: Solve

Find the x-intercepts of
Found 2 solutions by jim_thompson5910, janjan440:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Divide both sides by 4

Take the square root of both sides

-----------------------------------
Answer:

So the solution to is:

Which breaks down to:

or

Start with the given equation

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 . This is due to really looking like )

Plug in a=4, b=0, and c=-12

Square 0 to get 0

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

Now break up the fraction

or

Simplify

or (notice how these solutions are identical to the previous set of solutions)

So these expressions approximate to

or

So the x-intercepts of are

and

Answer by janjan440(1) (Show Source): You can put this solution on YOUR website!
If we look at the page numbers, we'll notice that they are consecutive integers. So they follow the algebraic form x, x%2B1, x%2B2, etc.

So if the product of two consecutive integers is 420, then we have the equation
x%28x%2B1%29=420

x%5E2%2Bx=420 Distribute

x%5E2%2Bx-420=0 Subtract 420 from both sides

%28x%2B21%29%28x-20%29=0 Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
x%2B21=0 or x-20=0
x=-21 or x=20 Now solve for x in each case

So our possible solutions are
x=-21 or x=20

However, since a negative page number is not possible, this means that the only solution is x=20

Now to find the next page number, simply add 1 to 20 to get

20%2B1=21

So the two page numbers are 20 and 21

Check:
To check this answer, simply multiply the two numbers:

20%2A21=420

420=420
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