Question

Solve 2x² – 3x - 20 = 0​

Answer 1

x=4

x=2.5

Explanation:

2x² - 3x - 20 = 0

assign a, b, and c using ax² + bx + c = 0

so a = 2

b = -3

and c = -20

then you plug that into the quadratic formula which gets you:

`x=\frac{-(-3)+\sqrt[]{(-3)^(2)-4*2*(-20) } }{2*2}`

It looks complicated but it's not so bad if you take it one step at a time

a negative negative is a positive, so that -(-3) in the front is just 3

Inside the square roots sign we can evaluate the power: -3 squared is 9

and -4 times 2 is -8 and -8 times -20 is 160

then on the bottom, 2 times 2 is 4

The equation is now

`x=(3+√(9+160) )/(4)`

9+160=169, and the square root of 169 is 13

`x=(3+13)/(4)`

3 + 13 = 16

16 divided by 4 is 4

so your first answer is 4

Now you have to do it again with a subtraction sign in front of the square root. The good thing is all the steps are the same until the last one. (We're not actually changing the contents of the root, just what we do with the result)

so when where we used to have
`x=(3+13)/(4)` its going to be
`x=(3-13)/(4)`

3- 13 = -10

and -10 divided by 4 = -2.5