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

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Answer 1 · 2017-08-07T14:39:21

$(x-2)(x-7)$

If we presume that the equation equals zero, then:

$x=2$ or $x=7$

$2x^2-13x+18-(x-2)^2$

We first expand the term $(x-2)^2$ .

$2x^2-13x+18-[x(x-2)-2(x-2)]$

$2x^2-13x+18-[x^2-2x-2x+4]$

$2x^2-13x+18-[x^2-4x+4]$

We now open the brackets, changing the signs appropriately.

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

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

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

$x^2-9x+14$

Factorise.

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

$x(x-7)-2(x-7)$

$(x-2)(x-7)$

If we presume that the equation equals zero, then:

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

$x=2$ or $x=7$

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