Question

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

Answer 1

Answer:

No real solutions;

$x=i+1.5$

Step-by-step 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 ($\sqrt{-1}$).

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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)

÷$2$           ÷

$x=\frac{2i+3}{2}$

Simplify,

$x=i+1.5$