What are the solutions of $x^2 - 2x + 9 = 0$ in simplest $a + bi$ form?

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Answer 1 · 2016-01-28T03:47:05

The roots are $-1/2-sqrt8/2i and -1/2+sqrt8/2i$

For the quadratic equation, $x^2-2x+9=0$ , we can use the quadratic formula:

$x=(-b+-sqrt(b^2-4ac))/(2a)$

$= (2+-sqrt((-2)^2-4*1*9))/(2*(-2)$

$= (2+-sqrt(-32))/-4$

$= (2+-sqrt(32)*sqrt(-1))/-4$

We represent $sqrt(-1)$ as $i$ and simplify $sqrt32$ :

$= (2+-sqrt(4)*sqrt(8)*i)/-4$

$= (2+-2*sqrt(8)*i)/-4$

$=-1/2-sqrt8/2i and -1/2+sqrt8/2i$

What are the solutions of x^2 - 2x + 9 = 0x^2 - 2x + 9 = 0 in simplest a + bia + bi form?