How do you solve $x^2- x + 41$ using the quadratic formula?

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Answer 1 · 2018-07-19T22:26:42

$x=(1+isqrt163)/2$ and $x=(1-isqrt163)/2$

We can find the roots of any quadratic of the form $ax^2+bx+c$ with the Quadratic Formula

$bar( ul|color(white)(2/2)x=(-b+-sqrt(b^2-4ac))/(2a)color(white)(2/2)|)$

We have the quadratic $x^2-x+41$ , where $a=1, b=-1$ and $c=41$ . Plugging these values in, we get

$x=(1pmsqrt(1-4(1*41)))/2$

This simplifies to

$x=(1pmsqrt(-163))/2$ or

$x=1/2 pm sqrt(-163)/2$

We can rewrite $sqrt(-163)$ as $sqrt(163)*sqrt(-1)$ , or $isqrt3$ . Doing this, we now have

$x=(1+isqrt163)/2$ and $x=(1-isqrt163)/2$

Hope this helps!

How do you solve x^2- x + 41x^2- x + 41 using the quadratic formula?