Question

If x = -2 is a solution of the equation

x² = -x + c where c is a constant, what
is another value of x that satisfies the
equation?

Answer 1

If x = -2 is a solution of the equation x² = -x + c, we can substitute x = -2 into the equation and solve for the constant c:

(-2)² = -(-2) + c

4 = 2 + c

Now, solve for c:

c = 4 - 2

c = 2

So, when c is 2, the equation x² = -x + c has a solution x = -2.

Now, let's find another value of x that satisfies the equation:

x² = -x + 2

To do this, you can rearrange the equation:

x² + x - 2 = 0

Now, you can factor this quadratic equation:

(x + 2)(x - 1) = 0

Setting each factor equal to zero and solving for x:

x + 2 = 0

x = -2

x - 1 = 0

x = 1

So, the equation x² = -x + 2 has two solutions: x = -2 and x = 1.