1Cademy - Solving $$(2x - 3)^2 = -12$$ Using the Square Root Property

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Square Root Property

Example

Solving $(2x - 3)^2 = -12$ Using the Square Root Property

Solve the equation $(2x - 3)^2 = -12$ using the Square Root Property. The squared binomial is already isolated, so apply the Square Root Property directly to obtain $2x - 3 = \pm\sqrt{-12}$ . Simplify the radical to introduce the imaginary unit, resulting in $2x - 3 = \pm 2\sqrt{3}i$ . Next, add $3$ to both sides to get $2x = 3 \pm 2\sqrt{3}i$ . Divide both sides by $2$ to isolate $x$ , yielding $x = \frac{3 \pm 2\sqrt{3}i}{2}$ . Rewrite in standard complex form to show the two individual solutions: $x = \frac{3}{2} + \sqrt{3}i$ and $x = \frac{3}{2} - \sqrt{3}i$ .