Question

Use the quadratic formula to find both solutions to the quadratic equation

given below.
x² + 8x = 20
O A. x - ³-√²7
2
B. X=2
□ C. x = -6-√27
D. x=-10
E. x = -1
F.
X=
-6+ √27
2

Answer 1

B. x=2 and D. x=-10

Explanation:

We have the quadratic formula:
`x=\frac{-b\sqrt{b^(2) -4ac} }{2a}`

Quadratic equations are in the form
`ax^2+bx+c`

We have to get the equation equal to zero before we can use the quadratic formula so subtract 20 from both sides and we get
`x^2+8x-20=0`

`a=1, b=8, c=-20`

Now we plug these values into the quadratic equation

`x=\frac{-8\sqrt{8^(2)-4(1)(-20) } }{2(1)}`

Now we solve for x

`x=(-8√(64+80) )/(2)`

`x=(-8√(144) )/(2)`

Now we get two equations because the square root gives us both a positive and a negative answer.

`x=((-8)+12)/(2)` and
`x=((-8)-12)/(2)`

Let's solve the first one now

`x=(4)/(2)`

`x=2`

Now the second one

`x=(-20)/(2)`

`x=-10`

so
`x=2` and
`x=-10`

so the answers are B and D.

Hope this helps!