Question

02.03) identify all of the following solutions of square root of x plus 10 end root minus 4 equals x . (1 point) x = −6 x = −1 x = −6 and x = −1 none of the above

Answer 1

$\sqrt{x+10}-4=x\\ \sqrt{x+10}=x+4\\x+10=(x+4)^2=x^2+8x+16\\x^2+7x+6=0\\x^2+x+6x+6=0\\x(x+1)+6(x+1)=0\\(x+6)(x+1)=0\\x=-6 \ and \ x=-1$

x = -6 is an extraneous solution, Therefore, solution is x = -1.

Answer 2

Answer:

The solution of given equation are x = −6 x = −1.

Step-by-step explanation:

The given equation is

$\sqrt{x+10}-4=x$

Add 4 on both sides.

$\sqrt{x+10}=x+4$

Square both side.

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

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

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

$0=x^2+6x+x+6$

$0=x(x+6)+1(x+6)$

$0=(x+6)(x+1)$

Use zero product property and equate each factor equal to 0.

$x+6=0\Rightarrow x=-6$

$x+1=0\Rightarrow x=-1$

Therefore the solution of given equation are x = −6 x = −1.