SOLUTION: Please help me solve this equation the square root of x+6 = x+4

Algebra ->  Square-cubic-other-roots -> SOLUTION: Please help me solve this equation the square root of x+6 = x+4       Log On


   



Question 108155: Please help me solve this equation the square root of x+6 = x+4
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B6%29=x%2B4
%28x%2B6%29=%28x%2B4%29%5E2 Square both sides.
x%2B6=x%5E2%2B8x%2B16 Expand right hand side.
x%5E2%2B7x%2B10=0Group all terms on one side.
%28x%2B5%29%28x%2B2%29=0 Factor.
x=-2,-5
Check your answers.
sqrt%28x%2B6%29=x%2B4
sqrt%28-2%2B6%29=-2%2B4
sqrt%284%29=2
2=2
True statement. Good answer.
sqrt%28x%2B6%29=x%2B4
sqrt%28-5%2B6%29=-5%2B4
sqrt%281%29=-1
-1=-1
True statement, since %28-1%29%5E2=1. Good answer.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28+x%2B6%29+=+x%2B4+.... both sides raise to the second power
%28sqrt%28x%2B6%29%29%5E2+=+%28x%2B4%29%5E2
then you will have:
x%2B6+=+x%5E2+%2B+8x+%2B+16... move all terms on one side
and you will have:
x%5E2+%2B+8x+%2B+16+-+x+-+6+=+0
x%5E2+%2B+7x+%2B+10+=+0
now you can use quadratic equation to solve the problem:
x%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29

x%5B1%2C2%5D=%28-7+%2B-+sqrt+%287%5E2+-4%2A1%2A10+%29%29+%2F+%282%2A1%29

x%5B1%2C2%5D=%28-7+%2B-+sqrt+%2849+-40+%29%29+%2F+2
x%5B1%2C2%5D=%28-7+%2B-+sqrt+%289+%29%29+%2F+2
x%5B1%2C2%5D=%28-7+%2B-+3%29+%2F+2

x%5B1%5D=%28-7+%2B+3%29+%2F+2
x%5B1%5D=%28-4%29+%2F+2
x%5B1%5D=-2

x%5B2%5D=%28-7+-+3%29+%2F+2
x%5B2%5D=%28-10%29+%2F+2

x%5B2%5D=-5