Question

Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

square root of the quantity x plus 7 end quantity minus 1 equals x

Answer 1

Answer:

x = 3

Step-by-step explanation:

This is hard to explain so i'll show you the work

Answer 2

Given expression in the question is,

$\sqrt{x+7}-1=x$

Solve the expression by using algebraic rules,

$\sqrt{x+7}-1+1=x+1$

$(\sqrt{x+1})^2=(x+1)^2$

$x+7=(x+1)^2$

$x+7=x^2+2x+1$

$(x+7)-(x+7)=(x^2+2x+1)-(x+7)$

$x^2+x-6=0$

$x^{2}+3x-2x-6=0$

$x(x+3)-2(x+3)=0$

$(x+3)(x-2)=0$

Therefore, $x=-3,2$

For extraneous solutions substitute the values of x in the original expression,

For $x=-3$,

$\sqrt{x+7}-1=x$

$\sqrt{-3+7}-1=-3$

$\sqrt{4}-1=-3$

$2-1=-3$

$1=-3$

Therefore, $x=-3$ is an extraneous solution.

For $x=2$,

$\sqrt{2+7}-1=2$

$3-1=2$

$2=2$

Therefore, $x=2$ is the solution.

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