How do you solve #x^2 - 6x = 391# by completing the square?

Question

Nathan Axel · Accepted Answer

#x=23# or #x-17# In #x^2-6x=391# as the Left Hand Side is #x^2-6x#, we can make it a complete square (compare it with #(x-a)^2=x^2-2ax+a^2#) by adding **square of half the coefficient of #x#. As coefficient of #x# is #-6#, we need to add #(-6/2)^2=9#, to each side and then we have #x^2-6x+9=391+9=400# or #(x-3)^2=20^2# Hence either #x-3=20# or #x-3=-20# i.e. #x=23# or #x-17#

Savannah Anderson · Answer

undefined To solve the equation x^2 - 6x = 391 by completing the square, follow these steps:

1. Move the constant term to the other side of the equation:
   x^2 - 6x - 391 = 0

2. To complete the square, take half of the coefficient of x, square it, and add it to both sides of the equation:
   x^2 - 6x + (-6/2)^2 = 391 + (-6/2)^2
   x^2 - 6x + 9 = 391 + 9

3. Simplify both sides of the equation:
   x^2 - 6x + 9 = 400

4. Rewrite the left side of the equation as a perfect square trinomial:
   (x - 3)^2 = 400

5. Take the square root of both sides:
   x - 3 = ±√400

6. Solve for x:
   x - 3 = ±20
   x = 3 ± 20

7. Solve for the two possible values of x:
   x = 3 + 20 = 23
   x = 3 - 20 = -17

So, the solutions to the equation x^2 - 6x = 391 by completing the square are x = 23 and x = -17.