How do you factor $x^2 = x + 2$ ?

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Answer 1 · 2016-03-23T17:42:51

$color(green)( (x +1 ) ( x-2 )$ is the factorised form of the expression.

$x^2 = x+2$

$x^2 - x -2 = 0$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 1*(-2) = -2$

AND

$N_1 +N_2 = b = -1$

After trying out a few numbers we get $N_1 = -2$ and $N_2 =1$
$1*(-2) = -2$ , and $1+(-2)= -1$

$x^2 - x -2 = x^2 - 2x + 1x -2$

$= x ( x-2 ) + 1 (x-2)$

$(x-2)$ is a common factor to each of the terms

$=color(green)( (x +1 ) ( x-2 )$

How do you factor x^2 = x + 2 x^2 = x + 2 ?