Question

How do you solve `x^{2} + 5x + 4= x`?

Answer 1

Given: `x^2 + 5x + 4= x`

Subtract x from both sides:

`x^2 + 4x + 4= 0`

Factor:

`(x+2)(x+2) = 0`

This above shows that there is a repeated root at `x = -2`

Answer 2

`x=-2`

Explanation:

`"Rearrange the equation into standard form"`

`rArrx^2+4x+4=0larrcolor(blue)"in standard form"`

`"the factors of + 4 which sum to + 4 are + 2 and + 2"`

`rArrx^2+2x+2x+4=0larrcolor(blue)"split the middle term"`

`rArrcolor(red)(x)(x+2)color(red)(+2)(x+2)=0larrcolor(blue)"factor by grouping"`

`rArr(x+2)(color(red)(x+2))=0`

`rArr(x+2)^2=0rArrx=-2`