What are the roots of the equation x, squared, plus, 14, x, plus, 50, equals, 0x 
2
 +14x+50=0 in simplest a, plus, b, ia+bi form?

To find the roots of the quadratic equation \(x^2 + 14x + 50 = 0\) in the form \(a + bi\), we can follow these steps:

### 1. Identify the coefficients:
For the quadratic equation \(ax^2 + bx + c = 0\), we have:
- \(a = 1\)
- \(b = 14\)
- \(c = 50\)

### 2. Use the quadratic formula:
The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Substituting the values of \(a\), \(b\), and \(c\):

\[
x = \frac{-14 \pm \sqrt{14^2 - 4(1)(50)}}{2(1)}
\]

### 3. Calculate the discriminant:
\[
\text{Discriminant} = b^2 - 4ac = 14^2 - 4(1)(50) = 196 - 200 = -4
\]

### 4. Compute the roots:
Since the discriminant is negative, the roots will be complex numbers.

\[
x = \frac{-14 \pm \sqrt{-4}}{2}
\]

\[
x = \frac{-14 \pm 2i}{2}
\]

\[
x = -7 \pm i
\]

### 5. Express the roots in the form \(a + bi\):
The roots are:
\[
x_1 = -7 + i \quad \text{and} \quad x_2 = -7 - i
\]

So, the roots of the equation in simplest \(a + bi\) form are \(-7 + i\) and \(-7 - i\).

Would you like more details or have any questions? 

Here are 5 related questions you might be interested in:
1. How does the discriminant determine the nature of the roots?
2. Can you find the sum and product of the roots of this quadratic equation?
3. What are the roots of the equation \(x^2 + 6x + 13 = 0\) in \(a + bi\) form?
4. How can you factor a quadratic equation with complex roots?
5. What is the geometric interpretation of complex roots on the complex plane?

**Tip:** When the discriminant of a quadratic equation is negative, the roots are always complex and appear as conjugate pairs \(a + bi\) and \(a - bi\).

What are the roots of the equation x^2 + 14x + 50 = 0 in simplest a + bi form?

Discover how to solve the quadratic equation x^2 + 14x + 50 = 0 and express the roots in the form a + bi. This detailed solution covers algebraic concepts, the quadratic formula, and complex numbers. Perfect for students in Grades 9-11.

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