# How do you solve #\x ^ { 2} - 8x = 20#?

##### 2 Answers

#### Explanation:

Re-arrange to form a standard quadratic form

Find the factors of

where sum of factors =

and rearrange in the equation.

Setting each factor equal to

#### Explanation:

#"rearrange and equate to zero"#

#rArrx^2-8x-20=0#

#"factorise by 'splitting' the middle term"#

#rArrx^2+2x-10x-20=0larr" 2x - 10x = -8x"#

#"take out a common factor from each 'pair' of terms"#

#rArrcolor(red)(x)(x+2)color(red)(-10)(x+2)=0#

#"take out the common factor of " (x+2)#

#rArr(x+2)(color(red)(x-10))=0#

#"equate each factor to zero and solve"#

#x+2=0rArrx=-2larr" solution"#

#x-10=0rArrx=10larr" solution"#