How do you solve using the completing the square method # x(x - 2) = 5#?

Question

Abigail Allen · Accepted Answer

#x_1=1+sqrt6#

#x_2=1-sqrt6# We begin with the provided equation. #x(x-2) = 5# To make it a trinomial, expand it. #x^2-2x=5# The number #1# is derived from the numerical coefficient of x, which is #-2#. We add 1 to both sides of the equation. We divide -2 by 2 and square the result, which is 1. #x^2-2x+1=5+1# #(x-1)^2=6# Calculate the square roots of the equation's two sides. (x-1)^2) #sqrt=+-sqrt6# #x-1 = +-sqrt6# #x=+1+sqrt6# #x_1=1 plus sqrt6# #x_2=1/sqrt6# May God bless you all. I hope this explanation helps.

Savannah Anderson · Answer

undefined To solve the equation x(x - 2) = 5 using the completing the square method:

1. Expand the expression x(x - 2) to get x^2 - 2x.
2. Rearrange the equation to have the terms on one side equal to zero: x^2 - 2x - 5 = 0.
3. To complete the square, take half of the coefficient of x, square it, and add it to both sides of the equation.
4. Half of -2 is -1, and (-1)^2 equals 1. Add 1 to both sides: x^2 - 2x + 1 = 5 + 1.
5. Factor the left side as a perfect square trinomial: (x - 1)^2 = 6.
6. Take the square root of both sides: x - 1 = ±√6.
7. Add 1 to both sides to isolate x: x = 1 ± √6.