Answer:
[tex]\fbox{\begin{minipage}{4em}c = -14\end{minipage}}[/tex]
Step-by-step explanation:
Given:
A quadratic equation: [tex]x^{2} - 5x + c = 0[/tex], with [tex]x =-2[/tex] is a solution.
Solve for:
Value of c
Step 1: define the problem
If [tex]x = -2[/tex] is a solution of equation [tex]f(x) = 0[/tex], then [tex]f(-2) = 0[/tex]
Step 2: Perform the calculation
Substitute [tex]x = -2[/tex] into original quadratic equation, we have:
[tex](-2)^{2} - 5(-2) + c = 0[/tex]
Perform the square and multiplication:
[tex]4 + 10 + c = 0[/tex]
Transfer all of numbers to the right side, except c:
(notice for the change in sign of numbers)
[tex]c = (-4) + (-10)[/tex]
Perform the sum on the right side to get c:
[tex]c = -14[/tex]
Hope this helps!
:)
