Question

finding solutions using the square root property
what are the solutions of the quadratic equation $49x^2 = 9$?
$\bigcirc$ $x = \frac{1}{9}$ and $x = -\frac{1}{9}$
$\bigcirc$ $x = \frac{3}{7}$ and $x = -\frac{3}{7}$
$\bigcirc$ $x = \frac{3}{4}$ and $x = -\frac{3}{4}$
$\bigcirc$ $x = \frac{9}{49}$ and $x = -\frac{9}{49}$

Explanation:

Step1: Isolate \(x^2\)

Divide both sides of the equation \(49x^2 = 9\) by 49.
\(x^2=\frac{9}{49}\)

Step2: Apply square root property

Take the square root of both sides. Remember that if \(x^2 = a\) (\(a\geq0\)), then \(x=\pm\sqrt{a}\).
\(x = \pm\sqrt{\frac{9}{49}}\)

Step3: Simplify the square root

Simplify \(\sqrt{\frac{9}{49}}\). Since \(\sqrt{9} = 3\) and \(\sqrt{49}=7\), we have \(\sqrt{\frac{9}{49}}=\frac{3}{7}\). So \(x=\pm\frac{3}{7}\), which means \(x = \frac{3}{7}\) and \(x=-\frac{3}{7}\).

Answer:

B. \(x=\frac{3}{7}\) and \(x = -\frac{3}{7}\) (assuming the second option is labeled B, if the original options had labels like A, B, C, D with the second option being B as per the order here)