Question

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

Answer 1

Answer:

$x=\frac{3\sqrt{2}-3 }{2}$

$x=-\frac{3\sqrt{2}-3 }{2}$

Step-by-step 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.

$x^2+3x=\frac{9}{4}$

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

$x^2 + 3x+ \frac{9}{4} =\frac{9}4} +\frac{9}{4}$

Factor:

$(x+\frac{3}{2})^2=\frac{9}{2}$

$x+\frac{3}{2} = \frac{3\sqrt{2} }{2 }$

or $x+\frac{3}{2} =-\frac{3\sqrt{2} }{2}$

So $x=\frac{3\sqrt{2}-3 }{2}$

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