Question

Which equation shows the quadratic formula used correctly to solve 5x2 + 3x – 4 = 0 for x?

Answer 1

5x^2+3x-4=0
x^2+3x/5-4/5=0
x^2+3x/5=4/5
x^2+3x/5+9/100=89/100
(x+3/10)^2=89/100
x+3/10=±(√89)/10
x=-3/10±√89/100
x=-3±(√89/10)

Answer 2

The equation
`x=(-3\pm √((3)^2-4(5)(-4)))/(2(5))` shows the quadratic formula used correctly to solve the given quadratic equation.

Explanation:

The given equation is

`5x^2+3x-4=0` .... (1)

If a quadratic equation is defined as

`ax^2+bx+c=0` ..... (2)

then the quadratic formula is

`x=(-b\pm √(b^2-4ac))/(2a)`

From equation (1) and (2), we get

`a=5,b=3,c=-4`

Using quadratic formula we get

`x=(-3\pm √((3)^2-4(5)(-4)))/(2(5))`

Therefore the equation
`x=(-3\pm √((3)^2-4(5)(-4)))/(2(5))` shows the quadratic formula used correctly to solve the given quadratic equation.