SOLUTION: hey there thanks for helpping... the question is...;x^4-10x^2=-24 thanks hope u can solve it

Question 203870: hey there thanks for helpping...
the question is...;x^4-10x^2=-24
thanks hope u can solve it

Found 2 solutions by Theo, PRMath:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

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let z =
equation becomes:

add 24 to both sides of this equation to get:

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This can be factored as follows:

your possible solutions are:
z = 6
z = 4
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if you let z = 6, then = 36 - 60 + 24 = 60 - 60 = 0 so z = 6 is a good answer.
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if you let z = 4, then = 16 - 40 + 24 = 40 - 40 = 0 so z = 4 is a good answer.
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this shows that your z equation has good answers.
you now need to go back to your x equation and see what answers are good for that.
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since you let z = x^2, this means that your possible solutions for x are:
= 6
= 4
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if you take the square root of both sides of these equations you get:
x = +/-
x = +/-
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you have 4 possible answers to your problem.
x =
x = -
x = = 2
x = - = -2
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you need to plug them into the original equation to see which ones fit.
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your original equation is after you added 24 to both sides of it which we did in the beginning.
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let x =
= 36 - 60 + 24 = 0
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let x = (- )
=
which equals 36 - 60 + 24 = 0
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let x = = 2
= = 16 - 40 + 24 = 0
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let x = (- = -2
= = 16 - 40 + 24 = 0
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looks like all values of x are good.
your answer would be:
x = +/-
and
x = +/- 2
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Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
Hey there..... see what you think of this......

Add 24 to both sides.

Now factor....

(If you use FOIL you can see this is correct)

BUT we are not done factoring

(See how we factored ?)

NOW we have to set EACH part of this equation equal to 0. So... here's how we do each part.........

(add 6 to both sides)
Take the square root of x and the square root of 6 to get...
x = the square root of 6

and.........

(x + 2) = 0
x = -2

and.........

(x - 2) = 0
x = 2

Do you need more explanation than this? I'm thinking you have had factoring and just got a little flustered because the exponents were bigger than you were used to seeing but if you need more explanation, just repost and I'll give you more.

I hope this helps.
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