Question

question\
what are the solution(s) of the quadratic below?\
$9x^2 - 4 = 0$\
answer attempt 1 out of 3\
additional solution no solution\
submit answer\
solutions)\
quadratic formula (rational)\
quadratic formula\
quadratic word problems (profit/gravity)\
interpret graphs of quadratics in context (graph given)\
interpret graphs of quadratics in context (graph given)\
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adratics review\
january 9 at 8:00 pm\
de: 82%\
this is the only question in this section.

Explanation:

Step1: Rearrange the equation

We start with the equation \(9x^{2}-4 = 0\). First, we add 4 to both sides of the equation to isolate the quadratic term.
\[9x^{2}=4\]

Step2: Solve for \(x^{2}\)

Next, we divide both sides of the equation by 9 to solve for \(x^{2}\).
\[x^{2}=\frac{4}{9}\]

Step3: Take square roots

To find the values of \(x\), we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution.
\[x=\pm\sqrt{\frac{4}{9}}\]

Step4: Simplify the square root

Simplifying the square root, we know that \(\sqrt{\frac{4}{9}}=\frac{\sqrt{4}}{\sqrt{9}}=\frac{2}{3}\). So,
\[x = \pm\frac{2}{3}\]

Answer:

\(x=\frac{2}{3}\) or \(x = -\frac{2}{3}\)