Question

what are the roots of x^2-3x+7=0

Answer 1

Use the quadratic equation -b +- sqrt(b^2 .....

Answer 2

x^2-3 x+7 = 0
Subtract 7 from both sides:
x^2-3 x = -7
Add 9/4 to both sides:
x^2-3 x+9/4 = -19/4
Factor the left hand side:
(x-3/2)^2 = -19/4
Take the square root of both sides:
abs(x-3/2) = (i sqrt(19))/2
Eliminate the absolute value:
x-3/2 = -(i sqrt(19))/2 or x-3/2 = (i sqrt(19))/2
Add 3/2 to both sides:
x = 1/2 (3-i sqrt(19)) or x-3/2 = (i sqrt(19))/2
Add 3/2 to both sides:
x = 1/2 (3-i sqrt(19)) or x = 1/2 (3+i sqrt(19))