Question

solve the equation using square roots. round your solutions to the nearest hundredth. -21 = 15 - 2x²

Explanation:

Step1: Isolate the squared term

Start with the equation \(-21 = 15 - 2x^2\). Subtract 15 from both sides to get \(-21 - 15 = -2x^2\), which simplifies to \(-36 = -2x^2\).

Step2: Solve for \(x^2\)

Divide both sides by -2: \(\frac{-36}{-2} = x^2\), so \(x^2 = 18\).

Step3: Take square roots

Take the square root of both sides: \(x = \pm\sqrt{18}\). Simplify \(\sqrt{18}\) as \(3\sqrt{2} \approx 4.2426\). So \(x \approx \pm 4.24\) (rounded to the nearest hundredth).

Answer:

\(x \approx 4.24\) or \(x \approx -4.24\)