Question

Solve the following equation by completing the square.
x(x-5)=14

Answer 1

`x_1=-2,\: x_2=7`

Explanation:

`x(x-5)=14\\\\x^2-5x=14\\\\x^2-5x+((-5)/(2))^2 =14+((-5)/(2))^2\\\\x^2-5x+(25)/(4)=14+(25)/(4)\\\\x^2-5x+(25)/(4)=(81)/(4)\\ \\(x-(5)/(2))^2=(81)/(4)\\ \\x-(5)/(2)=\pm(9)/(2)\\ \\x=(5)/(2)\pm(9)/(2)\\ \\x_1=-2,\: x_2=7`