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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve {{{4x^2=12}}} Find the x-intercepts of {{{f(x)=4x^2-12}}}      Log On


   

Question 130760: Solve 4x%5E2=12

Find the x-intercepts of f%28x%29=4x%5E2-12
Found 2 solutions by jim_thompson5910, janjan440:
Answer by jim_thompson5910(35256) About Me  (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





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Answer:

So the solution to is:




Which breaks down to:

or








4x%5E2-12=0 Start with the given equation

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


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve 4%2Ax%5E2-12=0 (notice a=4, b=0, and c=-12. This is due to 4%2Ax%5E2-12=0 really looking like 4%2Ax%5E2%2B0%2Ax-12=0)




x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A4%2A-12+%29%29%2F%282%2A4%29 Plug in a=4, b=0, and c=-12



x+=+%280+%2B-+sqrt%28+0-4%2A4%2A-12+%29%29%2F%282%2A4%29 Square 0 to get 0



x+=+%280+%2B-+sqrt%28+0%2B192+%29%29%2F%282%2A4%29 Multiply -4%2A-12%2A4 to get 192



x+=+%280+%2B-+sqrt%28+192+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)



x+=+%280+%2B-+8%2Asqrt%283%29%29%2F%282%2A4%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%280+%2B-+8%2Asqrt%283%29%29%2F8 Multiply 2 and 4 to get 8

So now the expression breaks down into two parts

x+=+%280+%2B+8%2Asqrt%283%29%29%2F8 or x+=+%280+-+8%2Asqrt%283%29%29%2F8


Now break up the fraction


x=0%2F8%2B8%2Asqrt%283%29%2F8 or x=0%2F8-8%2Asqrt%283%29%2F8


Simplify


x=sqrt%283%29 or x=-sqrt%283%29 (notice how these solutions are identical to the previous set of solutions)


So these expressions approximate to

x=1.73205080756888 or x=-1.73205080756888


So the x-intercepts of y=4%2Ax%5E2-12 are

x=1.73205080756888 and x=-1.73205080756888

Answer by janjan440(1) About Me  (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