Question

Use the quadratic formula to solve the equation.

x² - x = -2

Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Answer 1

x^2 - x = -2 can be rewritten as
x^2 - x + 2 = 0
observing, the given equation is not factorable, thus we use the quadratic equation:
x = [-b +- sqrt(b^2 - 4ac)]/(2a)
where
a = numerical coefficient of x^2
b = numerical coefficient of x
c = constant
substituting,
x = [ -(-1) +- sqrt((-1)^2 - 4(1)(2))]/(2(1))
x = [1 +- sqrt(1-8)]/2
x = [1 +- sqrt(-7)]/2
note that sqrt(-1) = i , thus we can rewrite this as
x = [1 +- i*sqrt(7)]/2
separating into plus and minus,
x = [1 + i*sqrt(7)]/2 and
x = [1 - i*sqrt(7)]/2

hope this helps~ :)

Answer 2

x^2 -x +2 = 0

a = 1
b = -1
c = 2

Use the quadratic formula

x = (1/2a)*([-b +/- sqrt(b^2 -4ac)]
= (1/2)[1 +/-sqrt(-7)]
= (1/2)[1 +/- i sqrt7]
= 1/2 + (i/2)sqrt7
or 1/2 - (i/2) sqrt7