To construct a quadratic equation, we start with the factored form:
(x - r1)(x - r2) = 0
where r1 and r2 are the roots of the quadratic equation.
In this case, we have the roots -5 (r1) and x = -2/9 (r2). Substituting these values, we get:
(x - (-5))(x - (-2/9)) = 0
Simplifying, we have:
(x + 5)(x + 2/9) = 0
Now, let's expand this equation to obtain the quadratic equation in the standard form:
x(x + 2/9) + 5(x + 2/9) = 0
x² + (2/9)x + (5/9)x + (10/9) = 0
Combining like terms, we have:
x² + (7/9)x + (10/9) = 0
Therefore, the quadratic equation with roots -5 and x = -2/9 is:
x² + (7/9)x + (10/9) = 0