SOLUTION: I can only solve part of this equation and then I get stuck. Can someone show me the next steps I need to take and explain how they are done? I have done the equation as far as I

Question 60914: I can only solve part of this equation and then I get stuck. Can someone show me the next steps I need to take and explain how they are done? I have done the equation as far as I can:
SQRT(2X-1)+SQRT(X-4)= 4 <----original equation
SQRT(2X-1)=4-SQRT(X-4)
(SQRT<2X-1>)^2 = (4-SQRT)^2
2X-1 = (4-SQRT)(4-SQRT) <------I am lost as to how to solve finish this side of the equation.
Thanks!
Found 2 solutions by funmath, joyofmath:
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
<----original equation

(x-5)(x-85)=0
x-5=0 and x-85=0
x=5 and x=85
Check for extraneous solutions:
Let x=5

4=4 x=5 is a valid solution.
let x=85

x=85 is an extraneous solution, it's not valid.
Therefore the solution is:
Happy Calculating!!!
Answer by joyofmath(189) (Show Source): You can put this solution on YOUR website!
The equation to solve is .
This is a quadratic equation in disguise!
The trick to solving these is to get all the square root stuff onto one side of the equation then square both sides. Then, you're left with a quadratic equation to solve:
Square both sides of the equation to solve:

This expands to:

Collect like terms:

Subtract 16 from both sides:

Subtract from both sides:

Now, square both sides:

Multiply things out:

Or
Subtract from both sides:

Subtract 16 from both sides:

Add 36x to both sides:

This is a quadratic equation that you can solve with the quadratic formula or by factoring the equation if you can see the factors:
The equation factors into
The roots of the equation are 85 and 5
If you plug 85 into your original equation it doesn't work but 5 does so is your answer.
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