SOLUTION: 2 times the square root of x minus 1 minus the square root of 3x minus 5 equals the square root of x minus 9

Question 202564: 2 times the square root of x minus 1 minus the square root of 3x minus 5 equals the square root of x minus 9
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Square both sides

Square the square root.

FOIL

Distribute

Combine like terms.

Get all the non-radical terms to one side

Combine like terms.

Combine the roots.

Divide both sides by -4.

Reduce

Square both sides

Square the square root

Square the right side

Multiply both sides by 4.

FOIL

Distribute

Subtract {{9x^2}}} from both sides.

Combine like terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible solutions are or

However, if you plug in into the original equation, you'll get a contradiction.

=====================================================================

Answer:

So the only solution is

RELATED QUESTIONS
what is the square root of x minus 2 minus 7 equals negative... (answered by ankor@dixie-net.com)

square root of 3x+1 minus the square root of... (answered by Fombitz)

y equals the square root of two x minus... (answered by Alan3354)

square root of 3x-5 minus square root x+7 equals... (answered by longjonsilver,AnlytcPhil)

the square root of x minus 3 square root of x with an index of 4 minus 4 equals... (answered by jsmallt9)

2 minus the square root of 5 divided by 16 minus the square root of... (answered by Alan3354)

square root of 2, minus 1, divided by the square root of 2, plus 1... (answered by Alan3354)

what is square root of 2/7 minus square root of 7/2? what is 5 square root 16/3 minus... (answered by checkley79)

solve (x-5)^2=7 A)-5+(minus underneath the plus) square root of 7 B) 5+(minus... (answered by tutorcecilia)