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 6 end quantity minus 4 equals x

-2 is a real solution to the equation

-5 is extraneous (not a solution to the original)

Step-by-step explanation:

sqrt(x+6)-4=x

Get square root thing by itself

Add 4 on both sides

sqrt(x+6)=x+4

Square both sides

x+6=(x+4)^2

x+6=x^2+8x+16

Subtract x and subtract 6 on both sides

0=x^2+7x+10

What two integers multiply to be 10 and add to be 7

Hope you said 2 and 5

0=(x+2)(x+5)

x=-2 or x=-5

Check!

x=-2 gives:

sqrt(-2+6)-4=-2

sqrt(4)-4=-2

2-4=-2

-2=-2 true so x=-2 is good

Check!

x=-5 gives:

sqrt(-5+6)-4=-5

sqrt(1)-4=-5

1-4=-5

-3=-5 not true so x=-5 is bad

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet