1Cademy - Solving $$2(x - 2)^2 + 3 = 57$$ Using the Square Root Property

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Square Root Property

Example

Solving $2(x - 2)^2 + 3 = 57$ Using the Square Root Property

Solve the equation $2(x - 2)^2 + 3 = 57$ using the Square Root Property. First, subtract $3$ from both sides to isolate the binomial term, resulting in $2(x - 2)^2 = 54$ . Then, divide both sides by $2$ to get $(x - 2)^2 = 27$ . Now apply the Square Root Property to obtain $x - 2 = \pm\sqrt{27}$ . Simplify the radical to $x - 2 = \pm 3\sqrt{3}$ . Finally, solve for $x$ by adding $2$ to both sides, yielding $x = 2 \pm 3\sqrt{3}$ . Rewrite to show the two individual solutions: $x = 2 + 3\sqrt{3}$ and $x = 2 - 3\sqrt{3}$ .