How do you solve #10-2(x-1)^2=4#?
3 Answers
Explanation:
This is in 'almost' completing the square format.
Subtract 10 from both sides
Lets make the LHS positive: Multiply both sides by (-1)
Divide both sides by 2
Square root both sides
Add 1 to both sides
If you change this to decimals you will introduce rounding errors so leave it as it is.
Explanation:
Move 10 to the other side and divide by 2
Take the square root.
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"#