SOLUTION: solve √6x-8=x 3√3x-1=2 2√x+2-3=7

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Question 669245: solve
√6x-8=x
3√3x-1=2
2√x+2-3=7
Found 2 solutions by vleith, MathLover1:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one. You can use the same process to solve the other 2
Get the term with radical by itself
sqrt%286%29x++=+x+%2B+8 note that I read your problem as sqrt%286%29+%2Ax+ not sqrt%286x%29. If the second one is what you want, then modify the following steps accordingly
now square both sides
%28sqrt%286%29x%29%5E2+=+%28x%2B8%29%5E2
simplify
%28sqrt%286%29%29%5E2+%2A+x%5E2+=+x%5E2+%2B+18x+%2B+64
6x%5Ex+=+x%5E2+%2B16x+%2B64
5x%5E2+-+16x+-+64+=+0
Solve using quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-16x%2B-64+=+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=%28-16%29%5E2-4%2A5%2A-64=1536.

Discriminant d=1536 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+1536+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+1536+%29%29%2F2%5C5+=+5.51918358845308
x%5B2%5D+=+%28-%28-16%29-sqrt%28+1536+%29%29%2F2%5C5+=+-2.31918358845308

Quadratic expression 5x%5E2%2B-16x%2B-64 can be factored:
5x%5E2%2B-16x%2B-64+=+5%28x-5.51918358845308%29%2A%28x--2.31918358845308%29
Again, the answer is: 5.51918358845308, -2.31918358845308. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-16%2Ax%2B-64+%29


then pick the solutions that 'make sense'

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1.
sqrt%286%29-8=x....move 8 to the right

sqrt%286%29=x%2B8....both sides raise to the power of two
%28sqrt%286%29%29%5E2=%28x%2B8%29%5E2
6=x%5E2%2B16x%2B64
0=x%5E2%2B16x%2B64-6
or
x%5E2%2B16x%2B58=0.....use quadratic formula

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

x+=+%28-16+%2B-+sqrt%28+16%5E2-4%2A1%2A58+%29%29%2F%282%2A1%29+

x+=+%28-16+%2B-+sqrt%28+256-232+%29%29%2F2+

x+=+%28-16+%2B-+sqrt%28+24+%29%29%2F2+

x+=+%28-16+%2B-+4.899%29%2F2+

solutions:
x+=+%28-16+%2B+4.899%29%2F2+

x+=+%28-11.101%29%2F2+

highlight%28x+=+-5.55%29+
or

x+=+%28-16+-+4.899%29%2F2+

x+=+%28-20.899%29%2F2+

highlight%28x+=+-10.45%29+

graph:
+graph%28+600%2C+200%2C+-20%2C+5%2C+-15%2C+75%2C+x%5E2%2B16x%2B58%29+

2.
3sqrt%283x%29-1=2....move -1 to the right
3sqrt%283x%29=2%2B1
3sqrt%283x%29=3....both sides raise to the power of two
%283sqrt%283x%29%29%5E2=3%5E2
9%283x%29=9
3x=9%2F9
3x=1
highlight%28x=1%2F3%29.........graph of a line that passes through the point
(1%2F3,0)
+graph%28+600%2C+200%2C+-5%2C+5%2C+-15%2C+15%2C+3sqrt%283x%29-3%29+

3.
2sqrt%28x%2B2%29-3=7....move -3 to the right

2sqrt%28x%2B2%29=7%2B3

2sqrt%28x%2B2%29=10....both sides raise to the power of two

%282sqrt%28x%2B2%29%29%5E2=10%5E2

4%28x%2B2%29=100
4x%2B8=100
4x=100-8
4x=92
x=92%2F4
highlight%28x=23%29........graph of a line that passes through the point
(23,0)


+graph%28+600%2C+200%2C+-15%2C+30%2C+-15%2C+15%2C+2sqrt%28x%2B2%29-10%29+