Answer:
\(\sqrt{100 - 4x^2} = 6\) are \(x = 4\) and \(x = -4\)
Explanation:
To solve the equation \(\sqrt{100 - 4x^2} = 6\), follow these steps:
1. Square both sides of the equation to eliminate the square root:
\[100 - 4x^2 = 6^2\]
\[100 - 4x^2 = 36\]
2. Subtract 100 from both sides:
\[-4x^2 = -64\]
3. Divide both sides by -4:
\[x^2 = 16\]
4. Take the square root of both sides:
\[x = \pm 4\]
So, the solutions for the equation \(\sqrt{100 - 4x^2} = 6\) are \(x = 4\) and \(x = -4\).