teach me how to complete the square when the x^2 value is higher than 1 please
STUDY THIS EXAMPLE SLOWLY AND CAREFULLY:
Solve for x:
4 x^2-8 x = 0
Divide both sides by 4:
x^2-2 x = 0
Add 1 to both sides:
x^2-2 x+1 = 1
Write the left hand side as a square:
(x-1)^2 = 1
Take the square root of both sides:
x-1 = 1 or x-1 = -1
Add 1 to both sides:
x = 2 or x-1 = -1
Add 1 to both sides:
Answer: |x = 2 or x = 0
Here's a pretty good tutorial on this topic :
http://www.purplemath.com/modules/sqrquad.htm
How about one like
3x^2 -10x +5 = 0 ? Gets kinda messy, but it is done the same way. DIvide thru by '3'
x^2 - 10/3 x = -5/3 Now take 1/2 of the 'x' term , square it and add to both sides
x^2 - 10/3 x + 100/36 = -5/3 + 100/36 simplify
(x-10/6)^2 = 40/36 Take the sqrt of both sides
x- 10/6 = +- sqrt (40/36)
x = 10/6 +- sqrt40 / 6 = (10 +- sqrt40)/6