Question

solve $2x^2 - 7 = -3$ using any method.
$x = \square$ and $x = \square$

Explanation:

Step1: Isolate the quadratic term

Start with the equation \(2x^2 - 7 = -3\). Add 7 to both sides to isolate the term with \(x^2\):
\(2x^2 - 7 + 7 = -3 + 7\)
Simplify: \(2x^2 = 4\)

Step2: Solve for \(x^2\)

Divide both sides by 2 to solve for \(x^2\):
\(\frac{2x^2}{2} = \frac{4}{2}\)
Simplify: \(x^2 = 2\)

Step3: Take square roots

Take the square root of both sides. Remember that a square root has two solutions (positive and negative):
\(x = \pm\sqrt{2}\)

Answer:

\(x = \sqrt{2}\) and \(x = -\sqrt{2}\)