A. solve for x by completing the square: x^2 + 2x = 8.
b. solve for p by completing the square: 7p^2 − 12p + 4 = 0.

a) x = 2 and -4 b) p = 4.12 and -2.4

Step-by-step explanation:

a) Using the completing the square me those to solve x²+2x = 8

firstly, we divide the equation by the coefficient of x² to give

x²+2x=8

Secondly, we need to get the constant of the equation x²+2x by adding the value gotten from dividing coefficient of x by 2 and squaring it i.e(2/2)² to give 1 as the constant

The equation becomes

x²+2x+1-1= 8

Note that 1 was subtracted just to ensure the question isn't altered

(x²+2x+1)-1 = 8

(x+1)(x+1)-1= 8

(x+1)(x+1)= 8+1

(x+1)² = 9

Squaring both sides of the equation

√(x+1)² = +/-√9

x+1 = +/-3

x = +3-1 = 2

x = -3-1 = -4

therefore x = 2 and -4

b) Using the same funny concept to solve the equation

7p² − 12p + 4 = 0

7p²-12p = -4

Dividing by coefficient of p²

p²-12/7p= -4/7

Completing the equation at the right hand side i.e p²-12/7p

We will add the square of half of the coefficient of p to both sides of the given equation (-12/7×1/2)² = (-12/14)²

= 144/196

p²-12/7p+144/196 = -4+144/196

(p-12/14)² = 640/196

Squaring both sides

√(p-12/14)² = +/-√640/196

p-12/14 = +/-3.26

p = +3.26+12/14 = 4.12

and p = -3.26+12/14 = -2.4

x=half

step-by-step explanation:

think about the doctor who treated the major and the speaker in the short story "in another country." put yourself in the shoes of the doctor, and based on what you read in the story, write what you think his thoughts about the major and the speaker would be. use the following vocabulary in your response and change the form of these words as needed: detached resign withered