Question

How do you solve `2x^2-9x+4=(2x-1)^2`?

Answer 1

`x = -3` or `x = 1/2`

Explanation:

`2x^2 - 9x + 4 = (2x - 1)^2`

We will start by expanding (FOILing ) the right-hand side of the equation:

`2x^2 - 9x + 4 = 4x^2 - 4x + 1`

Next, subtract `2x^2` from both sides:

`-9x + 4 = 2x^2 - 4x + 1`

Add `9x` to both sides:

`4 = 2x^2 + 5x + 1`

And now, subtract 4 from both sides:

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

This is a simple quadratic equation in `x` so we can solve it by completing the square or applying the quadratic formula or whatever method you prefer. I'll apply the quadratic formula:

`x = (-b ± sqrt(b^2 - 4ac))/(2a) = (-5 ± sqrt(5^2 - 4*2*(-3)))/(2*2)`

Simplification gives us:

`x = (-5 ± sqrt(49))/4`

Which further reduces to:

`x = (-5 ± 7)/4`

From here it should be easy to see that

`x = -3` or `x = 1/2`