Question

what are the solutions of this quadratic equation?
x² + 2x = -2
a. x = 1 ± i
b. x = -1 ± i
c. x = 0
d. x = ± i

Explanation:

Step1: Rewrite in standard form

Add 2 to both sides:
$$x^2 + 2x + 2 = 0$$

Step2: Use quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=1$, $b=2$, $c=2$:
$$x=\frac{-2\pm\sqrt{2^2-4(1)(2)}}{2(1)}$$

Step3: Calculate discriminant

Compute the radical term:
$$\sqrt{4-8}=\sqrt{-4}=2i$$

Step4: Simplify the expression

Substitute and simplify:
$$x=\frac{-2\pm2i}{2}=-1\pm i$$

Answer:

B. $x=-1 \pm i$