Question

Consider the quadratic equation below. 4x^2-5=3x+4 Determine the correct set-up for solving the equation using the quadratic formula.

Answer 1

`4x^2-5=3x+4`

`4x^2 - 3x - 5 - 4 = 0`

`4x^2 - 3x -9 = 0`

`x= (3 \pm √(3^2 - 4(4)(-9)))/(2(4))`

`x = \frac 1 8 (3 \pm √(9(1 + 16)))`

`x = \frac 1 8 (3 \pm 3√(17))`

Answer 2

Solutions are 1.92 and -1.17

Explanation:

The general solutions of quadratic equation of the form ax²+bx+c = 0 is given by
`(-b+√(b^2-4ac) )/(2a)` and
`(-b-√(b^2-4ac) )/(2a)`

Here the the equation is 4x²-5 = 3x + 4

On rearranging

4x²-3x-5-4 = 0

4x²-3x-9 = 0

Comparing with ax²+bx+c = 0, we will get a = 4, b = -3 and c = -9

The solutions are given by

`(-(-3)+√((-3)^2-4*4*(-9)) )/(2*4)` and
`(-(-3)-√((-3)^2-4*4*(-9)) )/(2*4)`

`(3+√(153) )/(8)` and
`(3-√(153) )/(8)`

1.92 and -1.17