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Al Khwarizmi lived from about 780 to about 850. His book on "completing and balancing" (solving equations) was published in about 830, when he would have been about 50 years old.
It is not correct to say that he "invented algebra", since "... we now know that his work is based on older Indian or Greek sources." (Rosen, Fredrick (1831). The Algebra of Mohammed Ben Musa. Kessinger Publishing. ISBN 1-4179-4914-7), quoted in the Wikipedia article linked below.
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