To solve for x in the equation √(2x + 2) − √x = 1, we can use algebraic manipulation to isolate x on one side of the equation. Here's how:
1. Start by adding √x to both sides of the equation:
√(2x + 2) = √x + 1
2. Square both sides of the equation to eliminate the square root:
(√(2x + 2))^2 = (√x + 1)^2
Simplifying the left side:
2x + 2 = x + 1 + 2√x + 1
3. Rearrange terms:
x - 2√x + 1 = 0
4. Factor the left side of the equation:
(√x - 1)^2 = 0
5. Solve for x by taking the square root of both sides:
√x - 1 = 0
√x = 1
x = 1^2 = 1
Therefore, the solution to the equation √(2x + 2) − √x = 1 is x = 1.