How to tell how many solutions c^2 - 18 = 9 in mental math?
a quadratic always has two solutions.
The answer key says 3+-square root 3
I think you mean
±3√3
The two solutions are √27 and -√27
But, √27 = √(9*3) = √9√3 = 3√3
Oh, okay. Thanks!
To determine the number of solutions of the equation c^2 - 18 = 9 mentally, we need to rearrange the equation and use mental calculations to solve it. Here are the steps:
1. Start by adding 18 to both sides of the equation: c^2 = 27.
2. To find the solutions, take the square root of both sides of the equation: √(c^2) = √27.
3. Simplifying the equation, we have |c| = √(9*3).
4. Since the square root of 9 is 3, we can rewrite the equation as |c| = 3√3.
5. Now, consider the equation |c| = 3√3. The absolute value of c will always be positive or zero, so we can drop the absolute value sign.
6. The equation simplifies to c = 3√3.
Thus, we have determined that the equation c^2 - 18 = 9 has only one solution, which is c = 3√3.