Question

How do you answer this?

Answer 1

`x=4+sqrt19` and `x=4-sqrt19`

Explanation:

Using complete the square:

Half term of `x`

`8/2=4x`

Put inside bracket and square it, adding on the constant.

`(x-4)^2-3`

Take away the squared number of the term of `x` in the bracket:

`(x-4)^2-16-3`

Collect like terms

`-16-3=-19`

`(x-4)^2-19`

This is the completed the square format, but now we solve.

`(x-4)^2-19=0`

Add `19`

`(x-4)^2=19`

Get rid of the squared bracket, by square rooting `19`.

Remember the `pm`

`x-4=pmsqrt19`

Add 4

`x=4pmsqrt19`

This means the answer will be either `x=4+sqrt19` and `x=4-sqrt19` as we usually have `2` solutions.

Answer 2

`x=4+-sqrt19`

Explanation:

`"solve using the method of "color(blue)"completing the square"`

`x^2-8x-3=0`

`• " the coefficient of the "x^2" term must be 1 which it is"`

`• " add/subtract "(1/2"coefficient of the x-term")^2" to"`
`x^2-8x`

`x^2+2(-4)xcolor(red)(+16)color(red)(-16)-3=0`

`rArr(x-4)^2-19=0`

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

`color(blue)"take the square root of both sides"`

`sqrt((x-4)^2)=+-sqrt19larrcolor(blue)"note plus or minus"`

`rArrx-4=+-sqrt19`

`"add 4 to both sides"`

`rArrx=4+-sqrt19larrcolor(red)"exact values"`