Answer:
The value of c is [tex]\frac{225}{4}[/tex].
Step-by-step explanation:
The perfect square of the difference between two numbers is:
[tex](x-y)^{2}=x^{2}-2xy+y^{2}[/tex]
The expression provided is:
[tex]x^{2}-15x+c[/tex]
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:
[tex]x^{2}-15x+c=(x-\sqrt{c})^{2}\\\\x^{2}-15x+c=x^{2}-2\cdot x\cdot\sqrt{c}+c\\\\15x=2\cdot x\cdot\sqrt{c}\\\\15=2\cdot\sqrt{c}\\\\\sqrt{c}=\frac{15}{2}\\\\c=[\frac{15}{2}]^{2}\\\\c=\frac{225}{4}[/tex]
Thus, the value of c is [tex]\frac{225}{4}[/tex].
