Question

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

Answer 1

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,


`\bf 2(x)[?]=8x\implies [?]=\cfrac{8x}{2x}\implies [?]=4`

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)

Answer 2

x²-8x=3
x²-8x+16=3+16=19
(x-4)²=19
x-4=±√19
x=4±√19
x=8.3589 approx or x=-0.3589 approx {4-√19,4+√19} or {-0.3589,8.3589}