To solve this equation, we first need to simplify the left side of the equation by distributing the -3x inside the square root:
√7 - 3x = x + 7
√7 - √(3x) = x + 7
Next, we need to isolate the square root term by moving all other terms to the other side of the equation:
√7 - √(3x) - x = 7
Now, we can square both sides of the equation to get rid of the square roots:
(√7 - √(3x) - x)^2 = 7^2
(√7 - √(3x) - x)(√7 - √(3x) - x) = 49
Expanding the left side of the equation, we get:
7 - 2√(7)(√(3x)) - 2√(7)(x) + 3x + 3x + 3x^2 = 49
Simplifying further, we get:
7 - 2√21√x - 2√7x + 9x + 3x^2 = 49
Rearranging terms, we get a quadratic equation:
3x^2 + 7x - 42 = 0
Now, we can solve this quadratic equation using the quadratic formula or by factoring it. After finding the solutions for x, we can substitute them back into the original equation to check for extraneous solutions.
To solve this equation, we first need to simplify the left side of the equation by distributing the -3x inside the square root:
√7 - 3x = x + 7
√7 - √(3x) = x + 7
Next, we need to isolate the square root term by moving all other terms to the other side of the equation:
√7 - √(3x) - x = 7
Now, we can square both sides of the equation to get rid of the square roots:
(√7 - √(3x) - x)^2 = 7^2
(√7 - √(3x) - x)(√7 - √(3x) - x) = 49
Expanding the left side of the equation, we get:
7 - 2√(7)(√(3x)) - 2√(7)(x) + 3x + 3x + 3x^2 = 49
Simplifying further, we get:
7 - 2√21√x - 2√7x + 9x + 3x^2 = 49
Rearranging terms, we get a quadratic equation:
3x^2 + 7x - 42 = 0
Now, we can solve this quadratic equation using the quadratic formula or by factoring it. After finding the solutions for x, we can substitute them back into the original equation to check for extraneous solutions.