Question

How do you solve `4k ^ { 2} - 104= 10k`?

Answer 1

`color(brown)(k=6.5 or color(brown)(k=-4`

Explanation:

`4k^2-104=10k`

`:.4k^2-10k-104=0`

`:.2(2k^2-5k-52)=0`

`:.(2k-13)(k+4)=0`

`:.2k=13` or `k=-4`

`:.k=13/2` or `k=-4`

`:.color(brown)(k=6.5` or `color(brown)( k=-4`

Answer 2

`x=6 1/2" "x=-4`

Explanation:

Write as: `4k^2-10k-104=0`

Note that all the values are even so divide everything by 2

`2k^2-5k-52=0`

Whole number factors of 52 are: `1xx52"; " 2xx26"; " 4xx13`

These will not work to give `-5k` so we have to use the formula or complete the square.

For a complete breakdown of the method for completing the square see: https://socratic.org/s/aF46CuxX

Using the formula:
`y=ax^2+bx+c" "->" "x=(-b+-sqrt(b^2-4ac))/(2a)`

Where: `a=2"; "b=-5"; "c=-52`

`x=(+5+-sqrt((-5)^2-4(2)(-52)))/(2(2))`

`x=5/4+-sqrt(441)/4`

`x=5/4+-21/4`

`x=6 1/2" "x=-4`