Question

How to solve 13. i)

Answer 1

Answer:

see below

Step-by-step explanation:

2x^2 +2x > -4

Add 4 to each side

2x^2 +2x+4 > -4+4

2x^2 +2x+4 > 0

Factor

2(x^2 +x+2) >0

Divide by 2

2/2(x^2 +x+2) >0/2

(x^2 +x+2) >0

Complete the square

Take the x coefficient divide by 2 and square it

(1/2) then square it  = 1/4

(x^2 + x +1/4) +7/4 >0

(x+1/2)^2 +7/4 >0

Subtract 7/4 from each side

(x+1/2)^2 +7/4 -7/4>0-7/4

(x+1/2)^2 >-7/4

This is always true since a quantity squared is greater than a negative quantity

x can be any number