Question

The difference of the square of a number and 4 is equal to 3 times that number. Find the negative solution.

Answer 1

The negative solution is x = –1.

Solution:

Let the number be x.

Square of a number = x²

3 times a number = 3x

Difference of square of a number and 4 = 3 times that number

`\Rightarrow x^2-4=3x`

Subtract 3x from both sides of the equation, we get

`\Rightarrow x^2-3x-4=0`

–3x can be written as x – 4x.

`\Rightarrow x^2+x-4x-4=0`

`\Rightarrow( x^2+x)+(-4x-4)=0`

1st bracket have common term x and bracket have –4 common term.

`\Rightarrow x( x+1)-4(x+1)=0`

Take common term x + 1 outside.

`(x+1)(x-4)=0`

By zero factor principle, if AB = 0 then A = 0 or B = 0.

x + 1 = 0, x – 4 = 0

x = –1, x = 4

The negative solution is x = –1.