Question

Solve for all real values of x.
x, squared, plus, 25, equals, 0
x
2
+25=
0


Solve the problem just like the example below
⬇️
Solve for all real values of x

x² - 16 = 0
+16. +16

x²=16

√x² = ± √16

x= ± 4

Solutions: x=4, x=-4

Answer 1

Let's solve the equation \( x^2 + 25 = 0 \) step by step.

1. **Set the equation:**
\[
x^2 + 25 = 0
\]

2. **Subtract 25 from both sides:**
\[
x^2 = -25
\]

3. **Take the square root of both sides:**
\[
\sqrt{x^2} = \pm \sqrt{-25}
\]

4. **Since the square root of a negative number involves imaginary numbers, we write:**
\[
x = \pm \sqrt{25}i
\]

5. **Simplifying gives:**
\[
x = \pm 5i
\]

The solutions are \( x = 5i \) and \( x = -5i \).

**Note:** There are no real solutions to this equation since \( x^2 = -25 \) has only imaginary solutions.

**Solutions:** \( x = 5i, x = -5i \) (no real solutions)