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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+-+10x%5E2+=+-24
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let z = x%5E2
equation becomes:
z%5E2+-+10z+=+-24
add 24 to both sides of this equation to get:
x%5E2+-+10z+%2B+24+=+0
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This can be factored as follows:
%28z-6%29+%2A+%28z-4%29+=+0
your possible solutions are:
z = 6
z = 4
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if you let z = 6, then z%5E2+-+10z+%2B+24 = 36 - 60 + 24 = 60 - 60 = 0 so z = 6 is a good answer.
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if you let z = 4, then z%5E2+-+10z+%2B+24 = 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:
x%5E2 = 6
x%5E2 = 4
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if you take the square root of both sides of these equations you get:
x = +/- sqrt%286%29
x = +/- sqrt%284%29
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you have 4 possible answers to your problem.
x = sqrt%286%29
x = - sqrt%286%29
x = sqrt%284%29 = 2
x = - sqrt%284%29 = -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 x%5E4+-+10x%5E2+%2B+24+=+0 after you added 24 to both sides of it which we did in the beginning.
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let x = sqrt%286%29
x%5E4+-+10x%5E2+%2B+24 = 36 - 60 + 24 = 0
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let x = (- sqrt%286%29)
x%5E4+-+10x%5E2+%2B+24 = %28-sqrt%286%29%29%5E4+-+10%2A%28-sqrt%286%29%29%5E2+%2B+24
which equals 36 - 60 + 24 = 0
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let x = sqrt%284%29 = 2
x%5E4+-+10x%5E2+%2B+24 = 2%5E4+-+10%2A2%5E2+%2B+24 = 16 - 40 + 24 = 0
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let x = (- sqrt%284%29 = -2
x%5E4+-+10x%5E2+%2B+24 = %28-2%29%5E4+-+10%2A%28-2%29%5E2+%2B+24 = 16 - 40 + 24 = 0
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looks like all values of x are good.
your answer would be:
x = +/- sqrt%286%29
and
x = +/- 2
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Answer by PRMath(133) About Me  (Show Source):
You can put this solution on YOUR website!
Hey there..... see what you think of this......

x%5E4+-+10x%5E2+=+-24 Add 24 to both sides.

x%5E4+-+10x%5E2+%2B+24+=+0 Now factor....

%28x%5E2+-+6%29%28x%5E2+-+4%29=+0 (If you use FOIL you can see this is correct)

BUT we are not done factoring

%28x%5E2+-+6%29%28x+%2B+2%29%28x+-+2%29+=+0 (See how we factored x%5E2+-+4 ?)

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

%28x%5E2+-+6%29+=+0 (add 6 to both sides)
x%5E2+=+6 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.