Question

Solve the quadratic equation X^2-5X÷2=0

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Answer 1

There are two possible solutions to this equation:

x = 0, x= 5

Explanation:

starting with the given equation, multiply both sides by "2" to get rid of the denominator:

`(x^2-5x)/(2) =0\\x^2-5x=0 * (2) \\x^2-5x=0`

Then extract "x" as a common factor on the left side.

`x^2-5x=0\\x\,(x-5)=0`

Notice that now you have a product of two factors [x is one, and the binomial (x-5) the other one] that equal zero. For such to happen, either factor must be zero. That is: x = 0, or (x-5) = 0.

So x=0 is a solution (renders 0 = 0 in the original equation)

The same is true for x = 5, it renders 0 = 0 in the original equation.