Question

Solve: (2x - 3)^2 = -4

Answer 1

No real solutions;

`x=i+1.5`

Explanation:

The easiest method to solve an algebraic equation is to use inverse operations. This applies to the given equation;

`(2x-3)^2=-4\\`

- Take the square root of both sides

`\sqrt{}`

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As one can see, the right side is a negative number. However, one cannot take the square root of a negative number and get a real result. Therefore, one must use imaginary numbers. Remember, the imaginary unit (
`i`) represents (
`√(-1)`).

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`2x-3=2i`

- Add (3) to undo the (-3)

`+3`

`2x=2i+3`

- Divide by (2) to remove the coefficient of (2x)

÷
`2` ÷

`x=(2i+3)/(2)`

Simplify,

`x=i+1.5`