Answer:
To solve the equation √(6x + 2) = 6x - 3, we need to isolate the radical term and then square both sides to eliminate the square root. Let's go through the steps:
Step 1: Isolate the radical term
√(6x + 2) = 6x - 3
Step 2: Square both sides of the equation
(√(6x + 2))^2 = (6x - 3)^2
Simplifying both sides:
6x + 2 = (6x - 3)(6x - 3)
6x + 2 = 36x^2 - 36x - 18x + 9
6x + 2 = 36x^2 - 54x + 9
Rearranging the equation:
36x^2 - 60x + 7 = 0
Now, we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 36, b = -60, and c = 7. Plugging these values into the quadratic formula:
x = (-(-60) ± √((-60)^2 - 4(36)(7))) / (2(36))
x = (60 ± √(3600 - 1008)) / 72
x = (60 ± √2592) / 72
x = (60 ± 51.2) / 72
Simplifying:
x = (60 + 51.2) / 72 ≈ 2.93
x = (60 - 51.2) / 72 ≈ 0.12
Therefore, the possible values of x that satisfy the equation √(6x + 2) = 6x - 3 are approximately x ≈ 2.93 and x ≈ 0.12.