Question

Solve x^2-8x=3 by completing the square. Which is the solution set of the equation?​

Answer 1

Question: x² - 8x = 3

First we factorise the x²-8x like so: (remember, you halve the 8 to get 4)

x² - 8x = 3

(x - 4)² - 16 = 3     .

(x - 4)² = 19

x - 4 = √19

x = 4±√19

Answer:

x = 4±√19

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Some explanations:

in:  (x - 4)² - 16 = 3

we have to subtract 16.

If we didn't,  then  (x - 4)² would expand to x² - 8x + 16

We don't want this since x² - 8x + 16 is not the same as x² - 8x, so we have to subtract 16 to make it the same:

x² - 8x = (x - 4)² - 16             but    x² - 8x $\neq$ (x - 4)²