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

3 Answers
Tony B
Mar 31, 2018

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.

t0hierry
Mar 31, 2018

x=1 +- sqrt(3)

Explanation:

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

Jim G.
Mar 31, 2018

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"

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