How do you factor $x^2 - x = 72$ ?

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Answer 1 · 2016-05-04T17:50:55

$color(green)(( x+8) ( x - 9)$ is the factorised form of the expression.

$x^2 - x = 72$

$x^2 - x - 72 = 0$

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

$N_1*N_2 = a*c = 1*(-72) = -72$

AND

$N_1 +N_2 = b = -1$

After trying out a few numbers we get $N_1 = -9$ and $N_2 =8$
$8*(-9) = -72$ , and $8+(-9)= -1$

$x^2 - x - 72 = x^2 - 9x +8x - 72$

$= x ( x - 9) + 8 (x - 9 )$

$= color(green)(( x+8) ( x - 9)$

How do you factor x^2 - x = 72x^2 - x = 72?