Question

The sum of a number and its square is zero. Write and solve an equation to find numbers that fit this description.

Short answer

The numbers that fit the given description are 0 and -1

Step-by-step solution

Write down the equation

The problem can be described by the following equation: \(x + x^2 = 0\), where \(x\) is the unknown number that we are trying to find.

Reformat the equation

Rearrange the equation into a format that can be easily solved. Since the equation \(x + x^2 = 0\) is a quadratic equation, you can rewrite it as \(x^2 + x = 0\)

Solve the equation

Now, to make it even easier, factor out an \(x\), giving us \(x(x + 1) = 0\). Apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. So, we set each factor equal to zero and solve for \(x\), getting the solutions \(x = 0\) or \(x = -1\)