Answer:
The value of c is 12.25
Step-by-step explanation:
we know that
A perfect square trinomial is of the form
[tex](x-a)^{2}=x^{2}-2ax+a^{2}[/tex]
In this problem we have
[tex]x^{2}-7x+c[/tex]
so
equate the equations
[tex]x^{2}-7x+c=x^{2}-2ax+a^{2}[/tex]
we have
the following equations
[tex]-7x=-2ax[/tex] -----> equation A
and
[tex]c=a^{2}[/tex] -----> equation B
Solve the equation A
[tex]-7x=-2ax[/tex]
[tex]7=2a[/tex]
[tex]a=3.5[/tex]
Solve the equation B
[tex]c=a^{2}[/tex]
[tex]c=3.5^{2}=12.25[/tex]
therefore
[tex](x-3.5)^{2}=x^{2}-7x+12.25[/tex]
The value of c is 12.25
Answer:
49/4
Step-by-step explanation:
To make x2-7x+c a perfect square trinomial we do it by completing the square method. First, make half of the coefficient of x then add and subtract by squaring it. c=49/4 this is the required value of c.
