How do you solve $2x^2-x=-5$ by completing the square?

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How do you solve $2x^2-x=-5$ by completing the square?

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Answer 1 · 2018-01-12T04:00:24

This question doesn't have any real solutions. However it does have two complex solutions;
$color(red)(x=(1+-isqrt(39))/4)$

Explanation:

$2x^2-x=-5$
$2x^2-x+5=0$
$2(x^2-x/2+5/2)=0$
$x^2-x/2+5/2=0$
$(x-1/4)^2-1/16+5/2=0$
$(x-1/4)^2+39/16=0$
$(x-1/4)^2=-39/16$
$x-1/4=+-sqrt(-39/16)$
$x-1/4=+-sqrt(-39)/4=+-(sqrt(39)xxsqrt(-1))/4$
$x=1/4+-(sqrt(39)xxsqrt(-1))/4=1/4+-(sqrt(39)xxi)/4$
$color(red)(x=(1+-isqrt(39))/4)$

I hope it helps :)

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How do you solve $2x^2-x=-5$ by completing the square?

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