Question

What is the solution set of 2x 2 - 3x = 5?

Answer 1

You use the quadratic formula:

`2x {}^(2) - 3x = 5`

`2x {}^(2) - 3x - 5 = 0`

`x = (3 + - √(9 -4(2)( - 5)))/(2 * 2)`

`x = (3 + - √(49) )/(4)`

`x = (3 + 7)/(4) \: and \: x = (3 - 7)/(4)`

`x = (5)/(2) \: and \: x = - 1`

Answer 2

Given the equation:

`2x^2-3x=5`

Subtract 5 from both sides we get;

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

Factorize the equation:

Break the middle term we get;

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

⇒
`x(2x-5)+1(2x-5)=0`

Take (2x-5) common we have;

`(2x-5)(x+1) = 0`

By zero product property we have;

`2x-5 = 0` or
`x+1 = 0`

⇒
`x = (5)/(2)` or x = -1

Therefore, the solutions for the given equation are:

`(5)/(2)`,
`-1`