(x+3)2=25 the (x+3) is squared

Question

(x+3) is squared and =25  I know the answer is 2,8 but can you show me how to work it out thank you so much.  solve by taking the square root  give the simplest form 

Answer 1

Hi Roseland;

Steve showed you the fast and easy way.

I will do the slow and complicated way.

(x+3)²=25

Let's FOIL the parenthetical equation...

(x+3)(x+3)

FIRST...(x)(x)=x²

OUTER...(x)(3)=3x

INNER...(3)(x)=3x

LAST...(3)(3)=9

x²+3x+3x+9=25

x²+6x+9=25

Let's subtract 25 from both sides...

x²+6x+9-25=25-25

x²+6x-16=0

For the FOIL...

FIRST must be (x)(x)=x²

OUTER and INNER must add-up to 6x.

LAST must be (16)(1) or (1)(16) or (2)(8) or (8)(2) or (4)(4) and one number must be negative to render the product of -16.

(x+8)(x-2)=0

Let's FOIL...

FIRST...(x)(x)=x²

OUTER...(x)(-2)=-2x

INNER...(8)(x)=8x

LAST...(8)(-2)=-16

x²-2x+8x-16=0

x²+6x-16=0

(x+8)(x-2)=0

Either or both parenthetical equation(s) must equal zero...

x+8=0, x=-8

x-2=0, x=2

Answer 2

(x+3)^2 = 25

 

Take square root of both sides:

 

|x+3| = 5

 

x+3 = ±5

 

x = -3 ± 5

 

x = -8 or 2