I don't understand how to get the answer to this "Radical equations" deal.
The problem I'm having trouble with is
(Square Root) x-5 = 2 (square root) 6
square both sides, then
(√(x-5))^2 = (2√6)^2
x-5 = 4(6)
x = 29
check:
Left Side = √(29-5
= √24
=√4 * √6
= 2√6 = Right Side
3index 4x-15+3=square6x
3(6x+7)= 3(x-5)
To solve a radical equation like the one you mentioned, you need to isolate the variable (in this case, x) on one side of the equation. Here's how you can solve it step-by-step:
1. Start by squaring both sides of the equation to eliminate the square root:
(Square Root) x-5)^2 = (2 (square root) 6)^2
2. Simplify:
x - 5 = 4 * 6
3. Continue simplifying:
x - 5 = 24
4. Next, add 5 to both sides of the equation to isolate the x-term:
x - 5 + 5 = 24 + 5
5. Simplify further:
x = 29
So, the solution to the equation is x = 29.
Remember, when squaring both sides of an equation, it is crucial to check the solution to ensure there isn't a case of extraneous solutions.