193k views
5 votes
Solve for all possible values of x.
√6x26x-3

1 Answer

0 votes

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.

User Heap
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories