find real solution.
3+ the square root of 3x+1 = x
To find the real solution of the equation 3 + √(3x + 1) = x, we can start by isolating the square root term on one side of the equation. Here are the steps:
1. Subtract 3 from both sides of the equation:
3 + √(3x + 1) - 3 = x - 3
√(3x + 1) = x - 3
2. Now, square both sides of the equation to eliminate the square root:
(√(3x + 1))^2 = (x - 3)^2
3x + 1 = x^2 - 6x + 9
3. Rearrange the equation to form a quadratic equation:
x^2 - 6x + 9 - 3x - 1 = 0
x^2 - 9x + 8 = 0
4. Solve the quadratic equation using factoring, completing the square, or the quadratic formula. In this case, we can factor the quadratic equation as:
(x - 1)(x - 8) = 0
Setting each factor equal to zero:
x - 1 = 0 or x - 8 = 0
Solving for x:
x = 1 or x = 8
Therefore, the real solutions to the equation 3 + √(3x + 1) = x are x = 1 and x = 8.