solve $x^{2}-8x = 20$ by completing the square. which is the solution set of the equation?\n{-22, 14}\n{-14…

solve $x^{2}-8x = 20$ by completing the square. which is the solution set of the equation?\n{-22, 14}\n{-14, 22}\n{-10, 2}\n{-2, 10}

solve $x^{2}-8x = 20$ by completing the square. which is the solution set of the equation?\n{-22, 14}\n{-14, 22}\n{-10, 2}\n{-2, 10}

Answer

Explanation:

Step1: Rewrite the equation

$x^{2}-8x = 20$

Step2: Complete the square

The coefficient of $x$ is $-8$. Half of it is $-4$, and its square is $16$. Add 16 to both sides of the equation: $x^{2}-8x + 16=20 + 16$ $(x - 4)^{2}=36$

Step3: Solve for $x$

Take the square - root of both sides: $x-4=\pm\sqrt{36}=\pm6$ When $x - 4 = 6$, $x=6 + 4=10$ When $x - 4=-6$, $x=-6 + 4=-2$

Answer:

{-2, 10}