# How do you solve 2x ^ { 2} - 13x + 18- ( x - 2) ^ { 2}?

Aug 7, 2017

#### Answer:

$\left(x - 2\right) \left(x - 7\right)$

If we presume that the equation equals zero, then:

$x = 2$ or $x = 7$

#### Explanation:

$2 {x}^{2} - 13 x + 18 - {\left(x - 2\right)}^{2}$

We first expand the term ${\left(x - 2\right)}^{2}$.

$2 {x}^{2} - 13 x + 18 - \left[x \left(x - 2\right) - 2 \left(x - 2\right)\right]$

$2 {x}^{2} - 13 x + 18 - \left[{x}^{2} - 2 x - 2 x + 4\right]$

$2 {x}^{2} - 13 x + 18 - \left[{x}^{2} - 4 x + 4\right]$

We now open the brackets, changing the signs appropriately.

$2 {x}^{2} - 13 x + 18 - {x}^{2} + 4 x - 4$

Group all like terms with their preceding signs and then simplify.

$2 {x}^{2} - {x}^{2} - 13 x + 4 x + 18 - 4$

${x}^{2} - 9 x + 14$

Factorise.

${x}^{2} - 7 x - 2 x + 14$

$x \left(x - 7\right) - 2 \left(x - 7\right)$

$\left(x - 2\right) \left(x - 7\right)$

If we presume that the equation equals zero, then:

$x - 2 = 0$ and $x - 7 = 0$

$x = 2$ or $x = 7$