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.)
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~ :)
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
To solve the equation x² - x = -2 using the quadratic formula, we can express the equation in the form ax² + bx + c = 0. In this case, a = 1, b = -1, and c = -2.
The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / (2a)
In our case, substituting the values of a, b, and c, we have:
x = (1 ± √((-1)² - 4(1)(-2))) / (2(1))
Simplifying further:
x = (1 ± √(1 + 8)) / 2
x = (1 ± √(9)) / 2
x = (1 ± 3) / 2
This gives us two solutions:
x₁ = (1 + 3) / 2 = 4 / 2 = 2
x₂ = (1 - 3) / 2 = -2 / 2 = -1
Therefore, the solutions to the equation x² - x = -2 using the quadratic formula are x = 2 and x = -1.