Question 1057496
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.