Precalc stuff..
square root of z-1= square root of z +6
are you solving for z? square both sides then solve for z.
that's my problem, i'm not sure how to solve for z. i need a process. it's not in my book or anything.
To solve the equation √(z-1) = √(z + 6), you can follow these steps:
1. Start by squaring both sides of the equation to eliminate the square roots. Squaring both sides gives you (z-1) = (z + 6).
2. Expand both sides of the equation. (z-1) is already fully expanded, so you don't need to do anything there. For (z + 6), the expansion is just z + 6.
3. Now, simplify the equation. Distribute the negative sign to the terms inside the parentheses on the left side to get z - 1 = z + 6.
4. Next, gather all the z terms on one side of the equation and the constant terms on the other side. Subtract z from both sides of the equation to move the z term from the right side to the left side. This gives you z - z - 1 = 6.
5. Simplify the equation further. The z term on the left side cancels out, so you're left with -1 = 6.
6. Since -1 is not equal to 6, this implies that there is no solution to the equation. Therefore, there is no value of z that satisfies the original equation.
In this case, squaring both sides of the equation led to a false statement, indicating that there is no solution. It's essential to check if any extraneous solutions arise when squaring both sides, as it can introduce solutions that do not satisfy the original equation.