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.

Answer: 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