Question

Solve the polynomial by completing the square. Show all steps of your work.
`2x^2 - 2x - 12 = 0`

Answer 1

you need to factor this problem, to do this you find the common values that add up to -2 and multiply to -24, which are -6 and 4 then you set it up from that

Answer 2

x = 3 x = -2

Explanation:

2
`x^(2)` - 2x - 12 = 0 Divide all the way through by 2

`x^(2)` -x - 6 = 0 Add 6 to both sides

`x^(2)` - x = 6 Take the b value of -1 and multiply that by 1/2 and then square your answer

(-1)(1/2) = -1/2 this squared is 1/4 Add 1/4 to both sides

`x^(2)` - x + 1/4 = 6 + 1/4

`(x -1/2)^(2)` =
`(24)/(4)` +
`(1)/(4)`

`(x -1/2)^(2)` =
`(25)/(4)`

`\sqrt{(x -1/2)^(2) }` = ±
`\sqrt{(25)/(4) }`

x - 1/2 = ± 5/2

x = 1/2 ± 5/2

x = 1/2 + 5/2

x = 6/2 = 3

x = 1/2 - 5/2 = -4/2 = -2