How does t^2-2t-1=0 become t=1+-sqrt2?

2 Answers
May 29, 2018

"see explanation"

Explanation:

"solve for t using the method of "color(blue)"completing the square"

• " the coefficient of the "t^2" term must be 1 which it is"

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

"add 1 to both sides"

t^2-2t=1

t^2+2(-1)t color(red)(+1)=1color(red)(+1)

(t-1)^2=2

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

sqrt((t-1)^2)=+-sqrt2larrcolor(blue)"note plus or minus"

t-1=+-sqrt2

"add 1 to both sides to obtain"

t=1+-sqrt2

An alternate way using the quadratic formula:

Explanation:

Another way to find solutions for t is to use the quadratic formula:

t = (-b \pm sqrt(b^2-4ac)) / (2a)

with a=1, b=-2, c=-1

t = (2 \pm sqrt((-2)^2-4(1)(-1))) / (2(1))

t = (2 \pm sqrt(4+4)) / 2

t = (2 \pm sqrt8) / 2

t = (2 \pm 2sqrt2) / 2

t = 1 \pm sqrt2