Question

Solve x2 - 8x = 3 by completing the square. which is the solution set of the equation ?

Answer 1

x²-8x=3
x²-8x+16=3+16=19
(x-4)²=19
x-4=±√19
x=4±√19
x=8.3589 approx or x=-0.3589 approx {4-√19,4+√19} or {-0.3589,8.3589}

Answer 2

we know that

`(x-a)^(2)=x^(2)-2ax+a^(2)`

in this problem we have

`x^(2) - 8x = 3`

so

equate

`-8x=-2ax\\2a=8\\a=4`

substitute

`(x-4)^(2)=x^(2)-8x+16`

therefore

`x^(2) - 8x = 3`

`x^(2) - 8x+16 = 3+16`

`x^(2) - 8x+16 = 19`

rewrite as perfect square

`(x-4)^(2) = 19`

`(x-4) =(+/-)√(19)\\x=(+/-) √(19)+4`

therefore

the answer is

the solution set is

`x1= 4+√(19)\\x2=4- √(19)`