Question

arrange these steps for solving a quadratic equation with complex solutions from first to last. (2 points) write the equation in standard form. apply the quadratic formula. identify coefficients a, b, and c. simplify the expression using $i = \sqrt{-1}$.

Explanation:

Step1: Write standard form

First, a quadratic equation must be in standard form ($ax^2 + bx + c = 0$) to proceed. So the first step is "Write the equation in standard form."

Step2: Identify coefficients

After standard form, we identify \(a\), \(b\), \(c\) from \(ax^2 + bx + c = 0\). So next: "Identify coefficients a, b, and c."

Step3: Apply quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\), which uses \(a\), \(b\), \(c\). So next: "Apply the quadratic formula."

Step4: Simplify with \(i\)

For complex solutions, when the discriminant is negative, we use \(i = \sqrt{-1}\) to simplify. So last: "Simplify the expression using \(i=\sqrt{-1}\)."

Answer:

1. Write the equation in standard form.
2. Identify coefficients a, b, and c.
3. Apply the quadratic formula.
4. Simplify the expression using \(i = \sqrt{-1}\).