Solve for all real values of x.

Question

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)