How do you solve 5x^2-10x=23 by completing the square?

1 Answer
Jim G.
May 21, 2018

x=1+-sqrt(28/5)

Explanation:

"using the method of "color(blue)"completing the square"

• " the coefficient of the "x^2" term must be 1"

"factor out 5"

5(x^2-2x)=23

• "add to both sides "(1/2"coefficient of x-term")^2

5(x^2+(-1)xcolor(red)(+1))=23color(red)(+5)larr"note"

rArr5(x-1)^2=28

rArr(x-1)^2=28/5

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

sqrt((x-1)^2)=+-sqrt(28/5)larrcolor(blue)"note plus or minus"

rArrx-1=+-sqrt(28/5)

"add 1 to both sides"

rArrx=1+-sqrt(28/5)larrcolor(red)"exact solutions"

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