Solve the equation for all values of x in simplest form: (x-9)^2=-49 Answer Attemptiout of 2 (A) Additional Solution (9)No Solution x=

To solve the equation $(x-9)^{2}=-49$, we need to find the values of $x$ that satisfy the equation.<br /><br />Step 1: Take the square root of both sides of the equation.<br />$\sqrt{(x-9)^{2}} = \sqrt{-49}$<br />$x-9 = \pm \sqrt{-49}$<br /><br />Step 2: Simplify the square root of -49.<br />$\sqrt{-49} = \sqrt{49} \cdot \sqrt{-1} = 7i$<br /><br />So, $x-9 = \pm 7i$<br /><br />Step 3: Solve for $x$.<br />$x = 9 \pm 7i$<br /><br />Therefore, the solutions to the equation $(x-9)^{2}=-49$ are:<br />$x = 9 + 7i$ and $x = 9 - 7i$<br /><br />Answer: $x = 9 + 7i$ and $x = 9 - 7i$