Question

Solve the equation by completing the square. If necessary, round to the nearest hundredth.

x² – 18x = 19

Answer 1

\[ x^2 -18x = 19\\ x^2 -18x+(\frac{18 }{ 2} )^2=19+(\frac{18 }{ 2} )^2\\ x^2 -18x+ 9 ^2 = 19 + 9 ^2 \\\\ x^2-18x+ 81 = 19+81\\\\ (x -9 )^2 = 100\\\\ x -9 = \pm \sqrt{100}\\\\ x = 9 \pm 10\\ x = 19\\ x = -1 \]