Square root of 4x-3=9

Answer 1

To solve the equation \(\sqrt{4x - 3} = 9\), we can follow these steps:

1. Square both sides to eliminate the square root:

   \[ (\sqrt{4x - 3})^2 = 9^2 \]

   This simplifies to:

   \[ 4x - 3 = 81 \]

2. Add 3 to both sides:

   \[ 4x = 81 + 3 \] \[ 4x = 84 \]

3. Divide both sides by 4:

   \[ x = \frac{84}{4} \] \[ x = 21 \]

Now, let's verify the solution by substituting \(x = 21\) back into the original equation:

\[ \sqrt{4(21) - 3} = \sqrt{84 - 3} = \sqrt{81} = 9 \]

Since both sides of the original equation are equal, the solution \(x = 21\) is correct.

Thus, the solution is:

\[ \boxed{21} \]