SOLUTION: Please help me solve this equation: sqrt(9x-5)=3x^2+2x+3

Algebra.Com
Question 829491: Please help me solve this equation: sqrt(9x-5)=3x^2+2x+3
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

Square both sides,





You can factor this equation,

Find solutions for both of those quadratic equations and then verify that they solve the original equation (because of the square root in the original equation).
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!


Square both sides:







   

   

There are no sign changes, so by Descartes' rule of signs,
there are no positive roots.

However any non-positive value of x would cause the left
side of the equation



to be the square root of a negative number, which is not a real 
number.

Therefore there are no real solutions.

Edwin
RELATED QUESTIONS

Please help me solve this equation step by step: {{{ sqrt(3+2x) + sqrt(2-2x=3)... (answered by lwsshak3)
Please help me solve this equation: {{{ int( sqrt(9x^2-x^4), dx, 0, 3 )... (answered by Fombitz)
Please help me solve this equation:{{{2x^4+3x^3+9x-7 divided by x^2+2x-1}}} (answered by Alan3354)
Please help me solve this equation {{{sqrt(3x-5)=7-sqrt(x +... (answered by scott8148)
Please help me solve this equation:... (answered by Alan3354)
Please help me solve the following equation. (3-2x)÷(sqrt ( 2x )-3)= (sqrt... (answered by Alan3354)
Please help me solve this equation: {{{... (answered by solver91311,Leaf W.)
Please help me solve this equation: Simplify as much as possible. x sqrt 32z^5 +... (answered by stanbon)
Please help me solve this equation: {{{ x^2-2x-3= sqrt( 4 )... (answered by edjones)