Answer:
[tex]x=\frac{3\sqrt{2}-3 }{2}[/tex]
[tex]x=-\frac{3\sqrt{2}-3 }{2}[/tex]
Step-by-step explanation:
Open the brackets first:
[tex]4x^2+9=18-12x[/tex]
Simplify:
[tex]4x^2+12x-9=0[/tex]
It is determined that this can't be factored, so rewrite the equation so you can complete the square.
[tex]x^2+3x=\frac{9}{4}[/tex]
Take the square of 1.5 and add it to both sides:
[tex]x^2 + 3x+ \frac{9}{4} =\frac{9}4} +\frac{9}{4}[/tex]
Factor:
[tex](x+\frac{3}{2})^2=\frac{9}{2}[/tex]
[tex]x+\frac{3}{2} = \frac{3\sqrt{2} }{2 }[/tex]
or [tex]x+\frac{3}{2} =-\frac{3\sqrt{2} }{2}[/tex]
So [tex]x=\frac{3\sqrt{2}-3 }{2}[/tex]
or [tex]x=-\frac{3\sqrt{2}-3 }{2}[/tex]
