How do you solve #x^2 + 2x = 3# by completing the square?

1 Answer
Mar 26, 2017

Answer:

Because the sign of the x term is positive, we use the pattern:
#(x+a)^2=x^2+2ax+a^2" [1]"#

Explanation:

Given: #x^2 + 2x = 3#

Add #a^2# to both sides:

#x^2 + 2x + a^2= 3 + a^2" [2]"#

Please observe that the left side of equation [2] now resembles the right side of equation [1]. This means that we can set the middle term of equation [1] equal to the middle term of equation [2], to find the value of "a":

#2ax = 2x#

#a = 1#

Substitute 1 for "a" in equation [2]:

#x^2 + 2x + 1^2= 3 + 1^2" [3]"#

Because we have completed the square, the left side of equation [3] collapses into a square with #a =1# and the right side becomes a single constant:

#(x + 1)^2 = 4" [4]"#

Perform the square root operation on both sides:

#x + 1 = +-2" [5]"#

Subtract 1 from both sides:

#x = -1 +-2" [6]"#

#x = 1 and x = -3#