Final Answer
$x=\frac{-1+\sqrt{3}i}{2},\:x=\frac{-1-\sqrt{3}i}{2}$
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Step-by-step Solution
Problem to solve:
$0=x^2+x+1$
Specify the solving method
1
Grouping terms
$-1=x^2+x$
Learn how to solve quadratic equations problems step by step online.
$-1=x^2+x$
Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation 0=x^2+x+1. Grouping terms. Rearrange the equation. Rewrite the equation. To find the roots of a polynomial of the form ax^2+bx+c we use the quadratic formula, where in this case a=1, b=1 and c=1. Then substitute the values of the coefficients of the equation in the quadratic formula: \displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.
Final Answer
$x=\frac{-1+\sqrt{3}i}{2},\:x=\frac{-1-\sqrt{3}i}{2}$