SOLUTION: HELP HELP HELP HELP ME PLEASE!!!!! {{{ sqrt( x-8 ) }}} = x-10

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Question 97624: HELP HELP HELP HELP ME PLEASE!!!!!
+sqrt%28+x-8+%29+ = x-10
Found 2 solutions by checkley71, bucky:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
SQRT(X-8)=X-10
SQUARE BOTH SIDES
X-8=X^2-20X+100
X^2-20X-X+100+8=0
X^2-21X+108=0
(X-12)(X-9)=0
X-12=0
X=12 ANSWER
X-9=0
X=9 ANSWER.

Answer by bucky(2100) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
sqrt%28x+-+8%29+=+x+-+10
.
Get rid of the radical on the left side by squaring both sides of the equation. On the left
side after squaring you just have x - 8 and on the right side you square the quantity (x - 10).
.
After squaring is completed the equation is:
.
x+-+8+=+x%5E2+-+20x+%2B+100
.
Let's get the equation in a more conventional form by merely switching (or transposing)
sides ... swapping the left and right sides to get:
.
x%5E2+-+20x+%2B+100+=+x+-+8
.
Get rid of the x on the right side by subtracting x from both sides. The result is:
.
x%5E2+-+21x+%2B+100+=+-8
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Now get rid of the -8 on the right side by adding 8 to both sides. When you do that the
equation reduces to:
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x%5E2+-+21x+%2B+108+=+0
.
This is quadratic equation in a conventional form. If you play with it a little, you will
find that it factors to become:
.
%28x-12%29%28x+-+9%29+=+0
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The left side of this equation will be zero (the same as the right side) if either of the
factors is equal to zero.
.
So possible answers come from setting each of the factors equal to zero to get:
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x+-+12+=+0
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which is solved by adding 12 to both sides to get:
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x+=+12
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and another solution is obtained from setting:
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x+-+9+=+0
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which can be solved by adding 9 to both sides to get:
.
x+=+9
.
So we have two possible answers ... x = 12 and x = 9.
.
Check both answers by returning to the equation that you were given and substitute
(one at a time) +12 for x and + 9 for x to see if they both work.
.
If you substitute +12 for x in the equation you were given you get:
.
sqrt%2812-8%29+=+12+-+10
.
which reduces to:
.
sqrt%284%29+=+12+-10
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and this furthermore reduces to:
.
2+=+2
.
So this answer checks.
.
Now try letting x = 9. Substitute 9 for x in the given equation and you get:
.
sqrt%289-8%29+=+9+-+10
.
This simplifies to:
.
sqrt%281%29+=+-1
.
but the square root of 1 is +1 and this does not equal -1. So the answer x = 9 does not
work out in the equation. Discard this answer. The only answer that satisfies the original
equation is x = 12.
.
Hope this helps you to understand the problem a little better.