Question

if using the method of completing the square to solve the quadratic equation x^2-1+x-38=0, which number would have to be added to "complete the square"?

Answer 1

`x^2\text{ -11x - 38 = 0}`

Step 1

Let the number to be added be = n

To make the equation a perfect square

`b^2\text{ = 4ac}`
`\begin{gathered} x^2\text{ - 11x - (38 + n) = 0} \\ a\text{ = 1, b = -11 , c = -(38 + n) = -38 - n} \end{gathered}`
`\begin{gathered} b^2\text{ = 4ac} \\ (-11)^2\text{ = 4 x 1 x (-38 - n)} \\ 121\text{ = 4(-38-n)} \\ 121\text{ = -152 - 4n} \\ 4n\text{ = -152 - 121} \\ 4n\text{ = -273} \\ n\text{ = }(-273)/(4) \end{gathered}`

The number is -273/4

`\text{.}`