Question

X² + 6x + 8 = 0
x = [? ], [ ]
Enter smallest solution first

Answer 1

`\sf \: x = - 2 \: \: or \: \: - 4`

Explanation:

`\sf {x}^(2) + 6x + 8 = 0`

Factorise.

`\sf {x}^(2) + 6x + 8 = 0 \\ \sf {x}^(2) + 4x + 2x + 8 = 0`

`\sf x(x + 4) + 2(x + 4) = 0 \\ \sf(x + 2)(x + 4) = 0`

Use the zero product property.

`\sf \: x + 2 = 0 \\ \sf \: x = 0 - 2 \\ \sf x = - 2`

Or

`\sf \: x +4 = 0 \\ \sf \: x = 0 - 4 \\ \sf \: x = - 4`

Therefore,

`\sf \: x = - 2 \: or \: \: - 4`

Answer 2

x = -4,-2

Explanation:

x² + 6x + 8 = 0

Factor the equation

(x+4)(x+2) =0

Using the zero product property

x+4 =0 x+2 =0

x=-4 x=-2

x = -4,-2