Question

How do you solve `5x ^ { 2} + 9x - 20= 4- 5x`?

Answer 1

Rearrange the expression so one side equals zero, then use the quadratic formula to find `x={-4,1.2}`

Explanation:

First, we'll rearrange the expression so the Right Hand Side (RHS) equals zero. This will give us our quadratic expression to use in the quadratic formula:

`5x^2+9x-20color(red)(-4)color(blue)(+5x)=cancel(4)color(red)(cancel(-4))cancel(-5x)color(blue)(cancel(+5x))`

`5x^2+9xcolor(blue)(+5x)-20color(red)(-4)=0`

`5x^2+14x-24=0`

Now, we'll utilize The Quadratic Formula. For any quadratic expression that looks like `ax^2+bx+c`:

`x=(-b+-sqrt(b^2-4ac))/(2a)`

For this case:

`a=5`
`b=14`
`c=-24`

Let's plug that in:

`x=(-14+-sqrt((14^2)-4(5)(-24)))/(2(5))`

`x=(-14+-sqrt(196-4(-120)))/10`

`x=(-14+-sqrt(196+480))/10`

`x=(-14+-sqrt(676))/10`

`x=(-14+-26)/10`

`x={(-14-26)/10,(-14+26)/10}`

`x={(-40)/10,12/10}`

`color(green)(x={-4,1.2})`