Question

User what is the extraneous solution for: √x+11 - 5 = x

Answer 1

To solve the equation √x+11 - 5 = x, isolate the square root term on one side of the equation, square both sides to eliminate the square root, expand and simplify the equation, factor the quadratic equation, and solve for x. The solution is x = -7 or x = -2.

Step-by-step explanation:

To solve the equation √x+11 - 5 = x, we need to isolate the square root term on one side of the equation. Here are the steps:

1. Add 5 to both sides of the equation: √x+11 = x + 5
2. Square both sides of the equation to eliminate the square root: (√x+11)2 = (x + 5)2
3. Expand both sides of the equation and simplify: x + 11 = x2 + 10x + 25
4. Rearrange the equation and simplify: x2 + 10x + 25 - x - 11 = 0
5. Simplify further: x2 + 9x + 14 = 0
6. Factor the quadratic equation: (x + 7)(x + 2) = 0
7. Set each factor equal to 0: x + 7 = 0 or x + 2 = 0
8. Solve for x: x = -7 or x = -2

Therefore, the solution to the equation is x = -7 or x = -2.