How do you solve x² - 2x = 15 by completing the square?

3 Answers
Jun 10, 2018

x=5 or x=-3

Explanation:

Although there is a better method, completing the square method is as such:

rearrange the formula to equate 0:

x^{2}-2x-15=0

(x-1)^2-1-15=0

Rearrange to get:

(x-1)^{2}=16

Square root on both sides to get:
(x-1) = +-4

Therefore adding 1 to both sides gives us either: x=5 or x=-3

Jun 10, 2018

x=5 and x=-3

Explanation:

x^2-2x-15=0 is in the format of ax^2+bx+c=0.

As c has already been moved to the left, let's add (b/2)^2 to both sides and factor:

x^2-2x=15
x^2-2x+(b/2)^2=15+(b/2)^2

Your value of b is the coefficient before the x in bx (from ax^2+bx+c=0):

x^2-2x+(-2/2)^2=15+(-2/2)^2
x^2-2x+(-1)^2=15+(-1)^2
x^2-2x+1=15+1
(x-1)(x-1)=16
(x-1)^2=16

Now solve for x:

x-1=+-sqrt16
x-1=+-4
x=4+1 and x=-4+1

Therefore, x=5 and x=-3

Jun 10, 2018

x=-3, x=5

Explanation:

x^2-2x-15=0

rArr (x-1)^2-1-15

rArr (x-1)^2-16=0

rArr (x-1)^2=16

rArr x-1=pmsqrt16

rArr x-1=pm4

rArr x=1pm4

rArr x=1-4 or x=1+4

rArr x=-3, x=5