Question

solve $-49x^2 + 4 = 0$ by using the square root method. enter the solution(s) in the box below as reduced fractions or integers. if there is more than 1 solution, separate the values with a comma (example: -11/7, 11/7).

Explanation:

Step1: Isolate \(x^2\) term

Start with the equation \(-49x^2 + 4 = 0\). Subtract 4 from both sides: \(-49x^2=-4\). Then divide both sides by \(-49\): \(x^2=\frac{-4}{-49}=\frac{4}{49}\).

Step2: Apply square root method

Take the square root of both sides. Remember that \(\sqrt{x^2}=\pm x\), so \(x = \pm\sqrt{\frac{4}{49}}\). Simplify the square root: \(\sqrt{\frac{4}{49}}=\frac{\sqrt{4}}{\sqrt{49}}=\frac{2}{7}\). Thus, \(x=\pm\frac{2}{7}\), which means \(x = \frac{2}{7},-\frac{2}{7}\).

Answer:

\(\frac{2}{7},-\frac{2}{7}\)