rzybert

25.05.2021 •

Mathematics

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Ответ:

nulledcracker12

31.03.2022

Mathematics

we have

(x+2)^2-2(x+2)-15=0

Let

u=(x+2)

Substitute

(u)^2-2(u)-15=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(u)^2-2(u)=15

Complete the square. Remember to balance the equation by adding the same constants to each side.

(u)^2-2(u)+1=15+1

(u)^2-2(u)+1=16

Rewrite as perfect squares

(u-1)^2=16

square root both sides

u-1=(+/-)4

u=1(+/-)4

u1=1+4=5

u2=1-4=-3

Find the solutions for the variable x

remember that

u=(x+2)

For u=5

5=(x+2)

x1=5-2=3

For u=-3

-3=(x+2)

x2=-3-2=-5

therefore

the answer is the option

x = –5 and x = 3

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