Question 416906
{{{ x+4=4sqrt(x+1)}}}...raise both sides to the power of two


{{{ (x+4)^2=(4sqrt(x+1))^2}}}


{{{ x^2+8x+16=16sqrt(x+1)^2}}}...cancel sqrt and power of two


{{{ x^2+8x+16=16(x+1)}}}


{{{ x^2+8x+16=16x+16}}}


{{{ x^2+8x-16x+16-16=0}}}


{{{ x^2-8x=0}}}


{{{ x(x-8)=0}}}..a product is equal to zero if any of multiplicands is equal to zero


{{{ x=0}}}.......first root


{{{ x-8=0}}}........{{{ x=8}}}..second root




check:

{{{ x+4=4sqrt(x+1)}}}.....plug in {{{ x=0}}}

{{{ 0+4=4sqrt(0+1)}}}

{{{ 4=4sqrt(1)}}}

{{{ 4=4*1}}}

{{{4=4}}}


{{{ x+4=4sqrt(x+1)}}}.....plug in {{{ x=8}}}

{{{ 8+4=4sqrt(8+1)}}}

{{{ 12=4sqrt(9)}}}

{{{ 12=4*3}}}

{{{12=12}}}