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

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

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Answer 1 · 2016-05-04T17:50:55

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

Explanation:

$x^{2} - x = 72$ $x^2 - x = 72$

$x^{2} - x - 72 = 0$ $x^2 - x - 72 = 0$

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

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot (- 72) = - 72$ $N_1*N_2 = a*c = 1*(-72) = -72$

AND

$N_{1} + N_{2} = b = - 1$ $N_1 +N_2 = b = -1$

After trying out a few numbers we get $N_{1} = - 9$ $N_1 = -9$ and $N_{2} = 8$ $N_2 =8$
$8 \cdot (- 9) = - 72$ $8*(-9) = -72$ , and $8 + (- 9) = - 1$ $8+(-9)= -1$

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

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

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

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

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