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

Sep 11, 2015

$x = - 3$ or $x = \frac{1}{2}$

#### Explanation:

$2 {x}^{2} - 9 x + 4 = {\left(2 x - 1\right)}^{2}$

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

$2 {x}^{2} - 9 x + 4 = 4 {x}^{2} - 4 x + 1$

Next, subtract $2 {x}^{2}$ from both sides:

$- 9 x + 4 = 2 {x}^{2} - 4 x + 1$

Add $9 x$ to both sides:

$4 = 2 {x}^{2} + 5 x + 1$

And now, subtract 4 from both sides:

$0 = 2 {x}^{2} + 5 x - 3$

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 $x = \frac{1}{2}$