Solve x2 – 8x = 3 by completing the square. which is the solution set of the equation?

X²-8x=3

we start off by grouping the "x"s, so

(x² - 8x) = 3

(x² - 8x + [?]²) = 3

now, we have a missing fellow, and the idea being, we use the middle term to get it, since we know that in a perfect square trinomial the middle term is just a product of left and right guys times 2, then,



so our missing fellow is 4, however all we're doing is borrowing from our very good friend Mr Zero, 0, so if we add 4², we also subtract 4².

(x² - 8x +4² - 4²) = 3

(x² - 8x + 4²) - 16=3

(x - 4)² = 19

x - 4 = ±√(19)

x = 4±√(19)