Question

Can someone give me a step by step solution to this radical equation please?? Im getting a migraine over it

Answer 1

Answer:

X=7,-4

Step-by-step explanation:

-3=(37-3x)^(1/2)-x

Add x to each side

X-3=(37-3x)^(1/2)

Change radical to root

X-3=sqrt(37-3x)

Square each side

(X-3)^2=37-3x

Expand the left side: (x-3)*(x-3)=x^2-6x+9

X^2-6x+9=37-3x

Add 3x to each side

X^2-3x+9=37

Subtract 9 from each side

X^2-3x=28

Make it =0: subtract 28 from each side

X^2-3x-28=0

Convert to product form (a)*(b)=0 so that by making either a or b zero you solve the equation. What two numbers add to -3 and multiply to -28? -7 and 4. So we get (x-7)*(x+4).

(X-7)*(x+4)=0

Now we just make x-7=0 or x+4=0.

(7)-7=0 or (-4)+4=0

X=7 or X=-4.