x^2 +x =-5
add 5 to each side
x^2 + x +5 = 0
now use the quadratic formula
x = -b +- sqrt(b^2 -4ac)
----------------------------
2a
where a=1 b=1 c=5
x = -1 +- sqrt(1^2 -4(1)(5))
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2(1)
x = -1 +- sqrt(-19)
----------------------------
2(1)
x = -1 +- i sqrt(19)
----------------------------
2(1)
x = -1/2 + sqrt(19)/2 *i
and
x = -1/2 - sqrt(19)/2 *i