Question

Solve the quadratic equation (2x-3)^2 = 6(3-2x)

Answer 1

`x=(3√(2)-3 )/(2)`

`x=-(3√(2)-3 )/(2)`

Explanation:

Open the brackets first:

`4x^2+9=18-12x`

Simplify:

`4x^2+12x-9=0`

It is determined that this can't be factored, so rewrite the equation so you can complete the square.

`x^2+3x=(9)/(4)`

Take the square of 1.5 and add it to both sides:

`x^2 + 3x+ (9)/(4) =\frac{9}4} +(9)/(4)`

Factor:

`(x+(3)/(2))^2=(9)/(2)`

`x+(3)/(2) = (3√(2) )/(2 )`

or
`x+(3)/(2) =-(3√(2) )/(2)`

So
`x=(3√(2)-3 )/(2)`

or
`x=-(3√(2)-3 )/(2)`