Respuesta :
Answer:
[tex]x=\frac{1+\sqrt{11}i}{2} ,\frac{1-\sqrt{11}i}{2}[/tex]
Step-by-step explanation:
1) Move all terms to one side.
[tex]3{x}^{2}-5x-10+3x-{x}^{2}+16=0[/tex]
2) Simplify [tex]3{x}^{2}-5x-10+3x-{x}^{2}+163x[/tex] to [tex]2x^2-2x+6.[/tex]
[tex]2x^2-2x+6=0[/tex]
3) Use the Quadratic Formula.
1) In general, given a[tex]a{x}^{2}+bx+c=0[/tex] there exists two solutions where:
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
2) In this case, [tex]a=2,b=-2[/tex] and [tex]c=6[/tex].
[tex]x=\frac{2+\sqrt{(-2)^2-4\times2\times6} }{2\times2} ,\frac{2-\sqrt{(-2)^2-4\times2\times6} }{2\times2}[/tex]
3) Simplify.
[tex]x=\frac{2+2\sqrt{11} i}{4} ,\frac{2-2\sqrt{11}i}{4}[/tex]
4) Simplify solutions.
[tex]x=\frac{1+\sqrt{11}i}{2} ,\frac{1-\sqrt{11}i}{2}[/tex]
Hope this helps,
- ROR
