Question

Solve the radical equation and what is the extraneous solution to the radical equation

Answer 1

Remove the radical by raising each side to the index of the radical.

x=-1

Answer 2

x = -6 and x= -1

Explanation:

the expression we have is:

`x+4=√(x+10)`

Taking tha square of the whole equation:

`(x+4)^2=x+10`

solving the binomial squared on the left side with the rule:

`(a+b)^2=a^2+2ab+b^2`

we get:

`x^2+8x+16=x+10`

rearranging all terms to the left:

`x^2+8x-x+16-10=0`

joining like terms:

`x^2+7x+6=0`

we can sove this quadratic equation with the quadratic formula, or by factoring:

`x^2+7x+6=(x+6)(x+1)=0`

and from this we find our two solutions using the zero product property (if a product of thing is equal to zero, one of them must be zero)

`x+6=0\\x=-6`

and

`x+1=0\\x=-1`