Final answer:
The equation r^(2)+9r+5=0 is a quadratic equation solved using the quadratic formula, yielding two possible solutions for r, which must be expressed correctly to the significant figures and units.
Step-by-step explanation:
The equation provided by the student, r^(2)+9r+5=0, is a quadratic equation which can be solved using the quadratic formula. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants, and x represents the unknown variable. Following the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), we can substitute our values from the equation r^(2)+9r+5=0 (a=1, b=9, c=5) to compute the solutions for r.
To apply the quadratic formula, we first determine the discriminant, which is √(b^2 - 4ac). After that, we plug this value into the quadratic formula to find the two possible values for r. These processes will lead us to compute the exact solutions for the quadratic equation, which should be expressed to the correct number of significant figures and proper units.