Question

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$x^{2}+4.0=0$$

Short answer

The solutions are \(x = 2i\) and \(x = -2i\).

Step-by-step solution

Rearrange the Equation

First we rearrange the given equation \(x^{2}+ 4.0 = 0\) to make it in the form something equals zero. This can be easily done by subtracting 4.0 from both sides of the given equation which gives the new equation as \(x^{2} = -4.0\)

Obtain the square root of the equation

To solve the value of \(x\), we need to find the square root of both sides. By doing so, we get \(x = \sqrt{-4.0}\)

Write the Solution as a Complex Number

The square root of a negative number is not defined in the real numbers, but it is defined in the complex numbers. The square root of -1 is 'i' in the complex numbers, therefore, we can rewrite the solution as \(x = \sqrt{4.0}\times i = 2.0i\). Since the squaring operation comes with a positive and a negative result, the final solution for the equation is \(x = 2i, x = -2i\)