| $X$ | $Y$ | $Xbd$ | $Yac$ | $(a,\,c)$ | $(b,\,d)$ |
| 1 | 4 | 4 | -1 | $\dfrac{1\pm 2}{2}$ | 2 |
| 1 | 4 | -1 | 4 | - | - |
| 4 | 1 | 4 | -1 | - | - |
| 4 | 1 | -1 | 4 | 2 | $\dfrac{1\pm 2}{2}$ |
"Find all real solutions" refers to finding all possible values of a variable that make an equation or inequality true. These values must be real numbers, meaning they can be positive, negative, or zero.
To find all real solutions, you must first rearrange the equation or inequality so that the variable is isolated on one side. Then, you can use algebraic techniques such as factoring or the quadratic formula to solve for the variable. It is important to check your solutions by plugging them back into the original equation to ensure they make the equation true.
Yes, an equation can have multiple real solutions. This is especially common in equations involving quadratic or cubic terms. It is important to carefully consider all possible values and check your solutions to ensure you have found all real solutions.
If you have carefully followed the steps to isolate the variable and solved for it correctly, you should have found all real solutions. To be sure, you can plug your solutions back into the original equation and see if they make the equation true.
Yes, there are a few special cases to consider when finding all real solutions. One is when the equation or inequality has an even power, which may result in two solutions (if positive) or no solutions (if negative). Another is when the equation or inequality has a variable in the denominator, which may result in extraneous solutions. It is important to be aware of these special cases and carefully check your solutions to ensure they are all real.