Question

Find the value of c that completes the square for x2−15x+c

Answer 1

The value of c is
`(225)/(4)`.

Explanation:

The perfect square of the difference between two numbers is:

`(x-y)^(2)=x^(2)-2xy+y^(2)`

The expression provided is:

`x^(2)-15x+c`

The expression is a perfect square of the difference between two numbers.

One of the number is x and the other is √c.

Use the above relation to compute the value of c as follows:

`x^(2)-15x+c=(x-√(c))^(2)\\\\x^(2)-15x+c=x^(2)-2\cdot x\cdot√(c)+c\\\\15x=2\cdot x\cdot√(c)\\\\15=2\cdot√(c)\\\\√(c)=(15)/(2)\\\\c=[(15)/(2)]^(2)\\\\c=(225)/(4)`

Thus, the value of c is
`(225)/(4)`.