Answer:
x = 3 or 7
Step-by-step explanation:
Solve by completing the square:
[tex]x^2 - 10x + 1 = -20[/tex]
First, move the constants to one side:
[tex]x^2 - 10x = -21[/tex]
Then, add [tex](\frac{-10}{2})^2[/tex] to both sides to make the right a perfect square trinomial, which is easy to factor:
[tex]x^2 - 10x + (\frac{-10}{2})^2 = -21 + (\frac{-10}{2})^2[/tex]
Simplify and Factor:
[tex]x^2 - 10x + 25 = -21 + 25[/tex]
[tex](x - 5)^2 = 4[/tex]
Finally, square root both sides using the even roots property:
[tex]\sqrt{(x - 5)^2} = \sqrt{4}[/tex]
x - 5 = ± 2
x = 5 ± 2
x = 3 or x = 7
