Question 343887
Each side of a square is 4 meters long. When each side is increased by x meters, the area os doubled. Find the value of x.

The area of a square is,
{{{A=s^2}}}
Initially,
{{{A[1]=4^2}}}
{{{A[1]=16}}}
.
.
.
{{{A[2]=(4+x)^2=32}}}
{{{16+8x+x^2=32}}}
{{{x^2+8x-16=0}}}
Use the quadratic formula,
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-8 +- sqrt( 8^2-4*1*(-16) ))/(2*1) }}} 
{{{x = (-8 +- sqrt( 64+64 ))/2 }}}
{{{x = (-8 +- 8sqrt( 2 ))/2 }}}  
{{{x = -4 +- 4sqrt(2) }}}
Only the positive answer makes sense in this situation.
{{{x = -4 + 4sqrt( 2 ) }}}   
 {{{highlight(x = 4( sqrt( 2 )-1)) }}}