Question

How to solve it and why

Answer 1

6.

4x^2 + 4 = 0

Divide both sides by 4

x^2 + 1 = 0

Use the quadratic formula since this cannot be factored.

x = (-b +- sqrt(b^2 - 4ac))/(2a)

x = +- sqrt(-4(1)(1))/2

x = +- sqrt(-4)/2

x = +- 2i/2

x = +- i

x = i or x = -i

Quicker solution:

If you have x^2 = number, then

x = +- sqrt(number)

Once you get to

x^2 + 1 = 0

Subtract 1 from both sides

x^2 = -1

Apply the quick method

x = +- sqrt(-1)

x = +- i

8.

2x^2 + 50 = 0

Divide both sides by 2

x^2 + 25 = 0

Subtract 25 from both sides

x^2 = -25

Apply quick method

x = +- sqrt(25)

x = +- 5i

x = 5i or x = -5i