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

Question

I need a step by step equation and explanation please.

Answer 1

sqrt(x+7)-1=x

sqrt(x+7) = x+1

x+7 = x² + 2x +1

x² + x - 6 = 0

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

Check that both roots solve the equation....otherwise you would have an extraneous root.

Yes, if what you find as a root, does not, in fact, satisfy the original equation, it is extraneous. In this case it gets introduced when you square both sides of the original equaton.

(x-1)(x+6)=x² + 5x -6...doesn't work.

You need to practice factoring...what I like to call unFOILing!