Final answer:
To make the equation congruent, we combine like terms and isolate the term containing the square root. Then, we square both sides of the equation to simplify further. The resulting equation can be solved using different methods such as factoring or rewriting as a quadratic equation.
Step-by-step explanation:
To make the equation congruent, we need to solve for the value(s) of x that satisfy the equation. First, we can simplify the equation by combining like terms:
3x + 4 = 2 + 2x + 2√2x + 1
3x - 2x - 2√2x = 2 + 1 - 4
x - 2√2x = -1
Next, we can isolate the term containing the square root:
-2√2x = -1 - x
Now, let's square both sides of the equation:
(-2√2x)² = (-1 - x)²
4x - 8√2x + 8x = 1 + x² + 2x + x²
4x + 8x - 1 - x² - 2x - x² = 8√2x
12x - 2 - 2x² = 8√2x
3x - 0.5 - 0.5x² = 2√2x
This equation can be solved using various methods, such as factoring, rewriting as a quadratic equation, or using the R method. Please let me know which method you prefer, and I can provide further guidance.