Question

How is the answer -2/3 and -4/3? I do not understand how this can be.

Answer 1

Read the full explanation below :)

Explanation:

First, set your equation equal to zero.

`9x^2+18x=(-8)` Add 8 to both sides. `darr`
`9x^2+18x+8=0`

Now, we simply use the quadratic formula.

`x_(1, 2)=(-b+-sqrt(color(blue)(b^2-4ac)))/(2a)`

First, solve for your discriminant, the portion marked in blue. Recall that a quadratic is written as `ax^2+bx+c`, so take the numbers from our original question using that formula.

`(18)^2-4(9)(8) = 36`

Now, plug that into the quadratic formula.

`x_(1, 2)=(-b+-sqrt(36))/(2a)`

Plug in the rest of your numbers.

`x_(1, 2)=(-18+-sqrt(36))/(2(9))`

Simplify.

`x_(1, 2)=(-18+-6)/18`

Solve.

`x_1=(-18+6)/18`
`x_1=(-12)/18 = (-0.666...) or (-2/3)`

`x_2=(-18-6)/18`
`x_2=(-24)/18 = (-1.333...) or (-1 1/3) or (-4/3)`

Answer 2

`"see explanation"`

Explanation:

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

`y=9x^2+18x+8=0`

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

`rArr9(x^2+2x+8/9)=0`

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

`rArr9(x^2+2(1)xcolor(red)(+1)color(red)(-1)+8/9)=0`

`rArr9(x+1)^2+9(-1+8/9)=0`

`rArr9(x+1)^2-1=0`

`rArr(x+1)^2=1/9`

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

`rArrx+1=+-sqrt(1/9)larrcolor(blue)"note plus or minus"`

`rArrx=-1+-1/3`

`rArrx=-1-1/3=-4/3" or "x=-1+1/3=-2/3`