How does an incomplete quadratic equation differ from a complete quadratic equation?

Answer 1

A complete quadratic equation is expressed in the form ax2+bx+c=0 (for example, 1x2-5x+4=0), and the formula to solve it is x1,2=(-b±√[b2-4ac])/2a {using the numbers from the example:

x1,2=(5±√[25-16])/2

x1,2=(5±√[9])/2

x1,2=(5±3)/2

So the answers will be 4 ([5+3]/2) and 1 ([5-3]/2).}

An incomplete quadratic equation can be expressed in two forms: ax2+bx=0 and ax2+c=0. The first form is solved by taking x (in some cases, x multiplied by a number that both a and b can be divided by, like in the next example) out of the two numbers, making the equation x(ax+b)=0. Then, either the outcome of the brackets (in the next example, the outcome of the brackets is x+1, so if x+1=0, then x=-1) or the x multiplying them needs to be zero in order for the equation to be correct, for example:

5x2+5x=0

5x(x+1)=0

x1=0

x2=(-1)

Or by taking out just x:

5x2+5x=0

x(5x+5)=0

x1=0

x2=(-1)

The second form is solved like a regular equation, for example:

2x2-162=0

2x2=162

x2=81

x=±9