SOLUTION: Using "Completing the Square" to find ALL solutions for: X^2-6x=40 How do you find ALL solutions?

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Question 1057496: Using "Completing the Square" to find ALL solutions for: X^2-6x=40
How do you find ALL solutions?
Answer by solve_for_x(190) (Show Source):
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Complete the square by adding the square of half of the coefficient of the "x"-term to both sides.

x^2 - 6x = 40

The coefficient of the x term is -6. Half of that is -3. And -3 squared is 9.

Adding 9 to both sides gives:

x^2 - 6x + 9 = 49

The left side can be factored as a perfect square:

(x - 3)^2 = 49

Taking the square root of both sides then gives:

x - 3 = �7

Adding 3 to both sides gives solutions for x:

x = 3 � 7

The solutions are:

x = 3 - 7 = -4

x = 3 + 7 = 10

Thus, the set of solutions is x = -4 and x = 10.

You can confirm this by rearranging the original equation as x^2 - 6x - 40 = 0, and then
using the Quadratic Formula to get the solutions for x.