How do you solve #10-2(x-1)^2=4#?

3 Answers
Mar 31, 2018

Answer:

#x=1+-sqrt(3)#

Explanation:

This is in 'almost' completing the square format.

Subtract 10 from both sides

#-2(x-1)^2=-6#

Lets make the LHS positive: Multiply both sides by (-1)

#+2(x-1)^2=+6#

Divide both sides by 2

#(x-1)^2=3#

Square root both sides

#x-1=+-sqrt(3)#

Add 1 to both sides

#x=1+-sqrt(3)#

If you change this to decimals you will introduce rounding errors so leave it as it is.

Mar 31, 2018

Answer:

#x=1 +- sqrt(3)#

Explanation:

Move 10 to the other side and divide by 2
#3 = (x-1)^2#
Take the square root.

Mar 31, 2018

Answer:

#x=1+-sqrt3#

Explanation:

#"isolate "(x-1)^2#

#"subtract 10 to both sides"#

#cancel(10)cancel(-10)-2(x-1)^2=4-10#

#rArr-2(x-1)^2=-6#

#"divide both sides by "-2#

#cancel(-2)/cancel(-2)(x-1)^2=(-6)/(-2)#

#rArr(x-1)^2=3#

#color(blue)"take the square root of both sides"#

#sqrt((x-1)^2)=+-sqrt3larrcolor(blue)"note plus or minus"#

#rArrx-1=+-sqrt3#

#"add 1 to both sides"#

#rArrx=1+-sqrt3larrcolor(red)"exact solutions"#