Final answer:
To solve the radical equation √6x+1=x−1, isolate the radical term and square both sides of the equation. Simplify the equation and solve the resulting quadratic equation.
Step-by-step explanation:
To solve the radical equation √6x+1=x−1, we need to isolate the radical term and square both sides of the equation to eliminate the square root. Here are the steps:
- Start with the equation √6x+1=x−1.
- Subtract x from both sides: √6x+1-x=x−1-x.
- This simplifies to √6x+1-x=0.
- Square both sides of the equation: (√6x+1-x)^2 = 0^2.
- Expand and simplify: 6x+2√6x+1+x^2-2x = 0.
- Combine like terms: x^2+4√6x-1 = 0.
- This is a quadratic equation. You can solve it using the quadratic formula.