√(X+10) + √(X-6) = 8
Help would be greatly appreciated! Thanks!
x=+-√(14
sqrt(x-6)+sqrt(x+10) = 8
sqrt(x-6) = 8 - sqrt(x+10)
Square both sides
x - 6 = (8 - sqrt(x + 10))^2
Expand out terms on the right hand side
x - 6 = x - 16sqrt(x + 10) + 74
16sqrt(x + 10) = 80
Divide both sides by 16
sqrt(x + 10) = 5
Square both sides
x + 10 = 25
x = 15
To solve the equation √(X+10) + √(X-6) = 8, we need to isolate the variable X. Here's how you can solve this equation step by step:
Step 1: Start by isolating one of the square roots. Let's isolate the square root containing X+10.
√(X+10) = 8 - √(X-6)
Step 2: Square both sides of the equation to remove the square root on the left side.
(√(X+10))^2 = (8 - √(X-6))^2
This simplifies to X+10 = 64 - 16√(X-6) + (X-6).
Step 3: Combine like terms. On the right side, we have -16√(X-6) and (X-6), which means we can combine them.
X+10 = 64 - 16√(X-6) + X - 6
Simplifying further, we get X+10 = X + 58 - 16√(X-6).
Step 4: Now, let's isolate the square root term by moving all other terms to the opposite side.
X - X + 10 - 10 = 58 - 16√(X-6)
This simplifies to 0 = 48 - 16√(X-6).
Step 5: Move the term with the square root to one side and simplify.
16√(X-6) = 48
Step 6: Divide both sides by 16 to solve for the square root.
√(X-6) = 3
Step 7: Square both sides to remove the square root.
(√(X-6))^2 = (3)^2
This simplifies to X - 6 = 9.
Step 8: Solve for X.
X = 9 + 6
X = 15
Therefore, the solution to the equation √(X+10) + √(X-6) = 8 is X = 15.