Final Answer
$x=\frac{1+\sqrt{83}i}{2},\:x=\frac{1-\sqrt{83}i}{2}$
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Step-by-step Solution
Problem to solve:
$x^2+21=x$
Specify the solving method
1
Grouping terms
$x^2+21-x=0$
Learn how to solve quadratic equations problems step by step online.
$x^2+21-x=0$
Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation x^2+21=x. Grouping terms. 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=21. Then substitute the values of the coefficients of the equation in the quadratic formula: \displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}. To obtain the two solutions, divide the equation in two equations, one when \pm is positive (+), and another when \pm is negative (-). Calculate the power \sqrt{-83} using complex numbers.
Final Answer
$x=\frac{1+\sqrt{83}i}{2},\:x=\frac{1-\sqrt{83}i}{2}$