Question

Solve each equation by completing the square. I need help with #9 show work too plsss

Answer 1

9) we get value of x:
`\mathbf{x=-4+√(42)\:i, x=-4-√(42)\:i}`

Option C is correct.

10) The difference is
`2k^3+3k-1`

Option A is correct.

Explanation:

9) We need to solve:

`x^2+8x+58=0`

Solving using quadratic formula:
`x=(-b\pm√(b^2-4ac))/(2a)`

We have a=1, b=8 and c=58

Putting values and finding value of x

`x=(-b\pm√(b^2-4ac))/(2a)\\x=(-8\pm√((8)^2-4(1)(58)))/(2(1))\\x=(-8\pm√(64-232))/(2)\\x=(-8\pm√(-168))/(2)\\We\:know√(-1)=i \\x=(-8\pm2√(42)\:i)/(2)\\x=(2(-4\pm√(42)\:i))/(2)\\x=(2(-4+√(42)\:i))/(2), x=(2(-4-√(42)\:i))/(2)\\x=-4+√(42)\:i, x=-4-√(42)\:i`

So, we get value of x:
`\mathbf{x=-4+√(42)\:i, x=-4-√(42)\:i}`

Option C is correct.

10)
`(5-2k^3-5k)-(-4k^2+6-8k)`

Combining like terms and subtracting:

`(5-2k^3-5k)-(-4k^3+6-8k)\\=5-2k^3-5k+4k^3-6+8k\\=-2k^3+4k^3-5k+8k+5-6\\=2k^3+3k-1`

The difference is
`2k^3+3k-1`

Option A is correct.