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
