Final answer:
The original cubic equation cannot be solved with the quadratic formula but requires numerical methods or other advanced techniques to find solutions. The quadratic formula and exponent rules are often used for quadratic equations and exponent manipulations, respectively.
Step-by-step explanation:
The equation 37467877109 = -30545993x²-111346x³ can be re-arranged to form a cubic equation by moving all the terms to one side to give 111346x³ + 30545993x² - 37467877109 = 0. To solve this type of equation, one would generally use numerical methods or factorization if possible, but it can't be solved using the quadratic formula directly as it's a cubic equation. However, computer software or graphing calculators are typically employed to find solutions to cubic equations.
To apply the mentioned methods, like the quadratic formula or operations involving exponents, we need to first identify if the equation can be simplified or factors can be found. For quadratic equations of the form ax² + bx + c = 0, the quadratic formula is -b ± √(b² - 4ac)/(2a). For cubic equations or higher, there is no simple formula and solutions are often found using numerical methods.
When dealing with exponents, to multiply exponents with the same base, we add the exponents. Similar rules apply for division, where the exponents are subtracted. Also, negative exponents represent the reciprocal, so x-n = 1/xn, and when an exponent is cubed, we multiply that exponent by 3.