Yes, this can be done this way:
(x-(-5))(x+a)=0, where a is any (positive or negative) number
This simplifies to: (x+5)(x+a) = 0
or written as quadratic: x2+(a+5)x+5a = 0
Solutions: x1 = -5 and x2 = -a,
so if a=5 the equation shortens to (x+5)2=0 ( or x2+10x+25=0 )
and there will be only one solution: x1,2 = -5
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The second difference of a quadratic equation being one indicates the second derivative at that point is positive. What you do from there depends on what property or transformation you're looking for with respect to the equation.
with the quadratic equation being ax2+bx+c and the formula being x=[-b±(b2-4ac)1/2]/2a just plug in the values for a b and c the quantity raised to the one half denotes a square root of that quantity.
It is the solution of a differential equation without there being any restrictions on the variables (No boundary conditions are given). Presence of arbitrary constants indicates a general solution, the number of arbitrary constants depending on the order of the differential equation.
b2 - 4ac72 - 4(1)(8)49 - 32= 17---------this tells us, by being positive, that there are two real roots in this quadratic .
There is no such thing as a quadric equation. The nearest word is quartic which is an equation involving the fourth power of the independent variable. It is unlikely that you will have come across that. It is possible that you might be wanting to refer to a quadratic equation, which is the equation of a parabola. That being the case, they two represent the same thing.