Respuesta :

Answer:

No real solutions;

[tex]x=i+1.5[/tex]

Step-by-step explanation:

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

[tex](2x-3)^2=-4\\[/tex]

- Take the square root of both sides

[tex]\sqrt{}[/tex]                

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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 ([tex]i[/tex]) represents ([tex]\sqrt{-1}[/tex]).

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[tex]2x-3=2i[/tex]

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

[tex]+3[/tex]          

[tex]2x=2i+3[/tex]

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

÷[tex]2[/tex]           ÷

[tex]x=\frac{2i+3}{2}[/tex]

Simplify,

[tex]x=i+1.5[/tex]

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