SOLUTION: what is the solution of the equation? sqrt(2x+13) -5 = x

Question 703695: what is the solution of the equation?
sqrt(2x+13) -5 = x
Answer by Nfrey78(18) (Show Source): You can put this solution on YOUR website!
what is the solution of the equation?

To solve a radical equation we first need to get the radical, i.e. square root, by itself
Add 5 to both sides to get

To "undo" the square root function, we need to do the inverse, which is square both sides. Notice that the square root is now undone

Squaring the right side is the same as (x + 5)(x + 5). Many students often make the mistake of saying it would be forgetting that they need to FOIL this expression out. Done correctly we should get

We can see this results in a quadratic, which means we have to set it to zero, moving everything to one side

Simplifying the right side by combining like terms yields

After set to zero we factor. What multiplies to give 12 but adds to 8?

Set each factor to zero
or
and solve for x to get our solutions!
or
RELATED QUESTIONS
find the real solutions of the equation. sqrt (3-2x=x what is the solution... (answered by london maths tutor)

what is the smallest positive integer of k such that the equation sqrt(x - 127) + sqrt(k... (answered by Edwin McCravy)

What is the extraneous solution of sqrt(x-3)= (x-5) also sqrt... (answered by jsmallt9)

2x +sqrt(x + 8) = 5 Is the solution... (answered by jim_thompson5910)

What is the solution for sqrt(2x + 1) + 5 = 2? (answered by tommyt3rd,dkppathak)

what is the solution to the following question: log base 4 of sqrt... (answered by josgarithmetic)

The solution for the equation, {{{ x+4 = sqrt (x^3-2x^2-5)+3 }}}, to the nearest... (answered by Fombitz,josgarithmetic)

the solution to 2x-2=5=13 is... (answered by Fombitz)

What is the solution set of the equation {{{ sqrt ( x+1 ) = x - 1 }}}? [Show... (answered by jrfrunner)