SOLUTION: (x+6)^(1/2)=(x-9)

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Question 214785: (x+6)^(1/2)=(x-9)
Found 2 solutions by drj, RAY100:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B6%29%5E%281%2F2%29=%28x-9%29

Step 1. Square both sides of the equation

%28%28x%2B6%29%5E%281%2F2%29%29%5E2=%28x-9%29%5E2

x%2B6=x%5E2-18x%2B81

Step 2. Subtract x+6 from both sides of the equation to get a quadratic one.

x%2B6-%28x%2B6%29=x%5E2-18x%2B81-%28x%2B6%29

0=x%5E2-19x%2B75

Step 3. We can use the quadratic formula to solve this given as

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

where a=1, b=-19 and c=75

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-19x%2B75+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-19%29%5E2-4%2A1%2A75=61.

Discriminant d=61 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--19%2B-sqrt%28+61+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+61+%29%29%2F2%5C1+=+13.4051248379533
x%5B2%5D+=+%28-%28-19%29-sqrt%28+61+%29%29%2F2%5C1+=+5.59487516204667

Quadratic expression 1x%5E2%2B-19x%2B75 can be factored:
1x%5E2%2B-19x%2B75+=+1%28x-13.4051248379533%29%2A%28x-5.59487516204667%29
Again, the answer is: 13.4051248379533, 5.59487516204667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-19%2Ax%2B75+%29



I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Step 2.

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
( x+6)^1/2 = (x-9),,,,,,square both sides
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(x+6) = (x^2 -18x +81)
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0 = x^2 -19x +75,,,,solve by quadratic formula
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a=1,,,,b=-19,,,,,c=75
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x=[ -(-19) +/- sqrt{ (-19)^2 - 4 (1)(75)} ] /2(1)
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x=[ 19 +/- sqrt{ 361 - -300)}] 2
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x= [ 19 +/- 7.810] /2
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x= 13.405,,5.595
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check,,,(5.595),,,,,,( 5.595 +6)^1/2 = 5.595 -9 = -3.405
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+/-3.405 =-3.405,,,,ok
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(13.405),,,,,,(13.405 +6)^1/2 = 13.405 -9 = 4.405
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+/- 4.405 = 4.405,,,,,,,,ok
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