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Solve the equation for all values of x in simplest form: (x-9)^(2)=-1

Solve the equation for all values of x \mathrm{x} in simplest form:\newline(x−9)2=−1 (x-9)^{2}=-1

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Quadratic equation with complex rootsright chevron icon

Full solution

Q. Solve the equation for all values of x \mathrm{x} in simplest form:\newline(x−9)2=−1 (x-9)^{2}=-1
  1. Simplify equation: Simplify the equation to isolate the squared term. \newline(x−9)2=−1(x-9)^2 = -1
  2. Take square root: Take the square root of both sides to solve for xx.\newlinex−9=±−1x - 9 = \pm\sqrt{-1}
  3. Recognize imaginary number: Recognize that −1\sqrt{-1} is an imaginary number, denoted as ii.x−9=±ix - 9 = \pm i
  4. Solve for x: Solve for x by adding 99 to both sides.\newlinex=9±ix = 9 \pm i

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