Final answer:
The quadratic equation -9d² + 8 = 0 is solved using the quadratic formula, resulting in the solutions d = 2 and d = -2.
Step-by-step explanation:
The equation provided, -9d² + 8 = 0, is a quadratic equation which is a type of polynomial equation in a single variable of the form ax² + bx + c = 0. To solve for the variable d, we can use the following steps:
- Rearrange the equation if necessary to have all terms on one side and set the equation to zero. In this case, the equation is already in the correct form.
- Identify the values of a, b, and c in the equation, which in this case are a = -9, b = 0, and c = 8.
- Apply the quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), to find the values of d.
- Insert the knowns into the formula. Since b = 0, the formula simplifies to d = ±√(-4ac) / (2a). In this case, it becomes d = ±√(-4(-9)(8)) / (2(-9)).
- Simplify the equation to get the actual values for d, ensuring that the results are expressed to the correct number of significant figures and proper units, if applicable. Here, since there are no units and we are working with integers, we just need to do the calculation to get the values for d.
- Eliminate terms wherever possible to simplify the algebra.
- Check the answer to see if it is reasonable.
- Multiply both sides by the same factor if necessary to make calculations easier, as recommended in some cases. For this particular equation, it is not necessary.
After performing the computation, we get: d = ±√(4*9*8) / (2*(-9)) = ±√(288) / (-18), which simplifies to d = ± 4 / -18. Hence, the two possible values for d are d = 4 / 18 or d = -4 / 18, which when simplified, give integer answers d = 2 or d = -2.