Question

2y² - 1 = 149

Explanation:

Step1: Add 1 to both sides

To isolate the term with \(y^2\), we add 1 to both sides of the equation \(2y^2 - 1 = 149\). This gives us \(2y^2 - 1 + 1 = 149 + 1\), which simplifies to \(2y^2 = 150\).

Step2: Divide both sides by 2

Next, we divide both sides of the equation \(2y^2 = 150\) by 2 to solve for \(y^2\). So, \(\frac{2y^2}{2}=\frac{150}{2}\), which simplifies to \(y^2 = 75\).

Step3: Take square root of both sides

To find the value of \(y\), we take the square root of both sides of the equation \(y^2 = 75\). Remembering that a square root has two solutions (positive and negative), we get \(y=\pm\sqrt{75}\). Simplifying \(\sqrt{75}\) as \(\sqrt{25\times3}=5\sqrt{3}\), so \(y = \pm5\sqrt{3}\) or approximately \(y\approx\pm8.66\).

Answer:

\(y = \pm5\sqrt{3}\) (or \(y\approx\pm8.66\))