Question

Solve the quadratic equation using the quadratic formula. x^2-6x+25=0





A
−7 and 1-7\ and\ 1−7 and 1

B
−1 and 7-1\ and\ 7−1 and 7

C
3±4i3\pm4i3±4i

D
3±2i343\pm2i\sqrt{34}3±2i
34
​

Answer 1

To solve the quadratic equation \(x^2 - 6x + 25 = 0\) using the quadratic formula, we can follow these steps:

1. **Identify coefficients**: The quadratic formula is given by \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a\), \(b\), and \(c\) are the coefficients from the equation \(ax^2 + bx + c = 0\).

For the equation \(x^2 - 6x + 25 = 0\):
- \(a = 1\)
- \(b = -6\)
- \(c = 25\)

2. **Calculate the discriminant**: We need to calculate \(b^2 - 4ac\):
\[
b^2 - 4ac = (-6)^2 - 4 \cdot 1 \cdot 25 = 36 - 100 = -64
\]

3. **Apply the quadratic formula**:
Since the discriminant is negative, this means the solutions will be complex:
\[
x = \frac{-(-6) \pm \sqrt{-64}}{2 \cdot 1} = \frac{6 \pm \sqrt{-64}}{2}
\]
\[
\sqrt{-64} = 8i
\]
So the equation becomes:
\[
x = \frac{6 \pm 8i}{2} = 3 \pm 4i
\]

Therefore, the solutions to the equation \(x^2 - 6x + 25 = 0\) are \(3 + 4i\) and \(3 - 4i\).

The correct choice from the options provided is:
**C \(3 \pm 4i\)**.