Question

What are the solutions of X²+25=0

Answer 1

Answer:   (no real solutions) but if its complex math it's:

x=  0.0000 + 5.0000

x=  0.0000 - 5.0000

Step-by-step explanation:    Solve  :    x2+25 = 0

Subtract  25  from both sides of the equation :

                     x2 = -25

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ -25  

In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1

Accordingly,  √ -25  =

                   √ -1• 25   =

                   √ -1 •√  25   =

                   i •  √ 25

Can  √ 25 be simplified ?

Yes!   The prime factorization of  25   is

  5•5

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 25   =  √ 5•5   =

               ±  5 • √ 1   =

               ±  5

The equation has no real solutions. It has 2 imaginary, or complex solutions.