SOLUTION: solve the radical equation. sqrt(4x+5)=2+sqrt(2x-1)

Question 464180: solve the radical equation. sqrt(4x+5)=2+sqrt(2x-1)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
solve the radical equation. sqrt(4x+5)=2+sqrt(2x-1)
...
√(4x+5)=2+√sqrt(2x-1)
move radicals to one side of the equation
√(4x+5)-√sqrt(2x-1)=2
square both sides: (a-b)^2=a^2-2ab+b^2)
4x+5-2√(4x+5)(2x-1)+2x-1=4
isolate radical
2√(4x+5)(2x-1)=6x+4-4=6x
square both sides again
4(4x+5)(2x-1)=36x^2
4(8x^2+6x-5)=36x^2
32x^2+24x-20=36x^2
-4x^2+24x-20=0
divide by -4
x^2-6x+5=0
(x+5)(x-1)=0
x=1
or
x=-5 (reject, (x≥-5/4), sqrt(4x+5) restriction
ans:
x=1
RELATED QUESTIONS
solve the following radical: {{{ sqrt ( 3x )+ sqrt ( 2x-1 ) = 5 / sqrt ( 2x-1 )... (answered by lwsshak3)

Solve the equation: sqrt(x+sqrt(4x+sqrt(16x+sqrt(64x+5))))-sqrt(x)=1 (answered by Fombitz)

sqrt(4x+5) = 2 +... (answered by Apathious)

Solve the radical equation... (answered by ankor@dixie-net.com)

Solve the equation. sqrt 2x + 5 - sqrt x - 2 =... (answered by Alan3354)

Solve the equation sqrt (2x + 5) - sqrt (x - 2) =... (answered by monika_p,Mathtut)

solve the following radical equation: {{{sqrt ( 3x+1 ) - sqrt ( 2x-10 )= 4... (answered by AnlytcPhil)

Solve the radical equation. [SQRT(2x^2 + 6x + 4)] = x +... (answered by harpazo)

1.) The solution to sqrt 2x+3 - sqrt x-1=1 is x=3? true or false 2.) The solution to... (answered by ikleyn)