Final answer:
To solve √3 + 7 = 6 + 4√s, isolate the variable by simplifying the equation step by step. The final solution is √s = -1/8 + s.
Step-by-step explanation:
To solve the equation: √3 + 7 = 6 + 4√s, we need to isolate the variable (√s).
Start by subtracting 6 from both sides of the equation: √3 + 7 - 6 = 6 + 4√s - 6. This simplifies to √3 + 1 = 4√s.
Next, subtract 1 from both sides of the equation to get √3 = 4√s - 1. Now, square both sides to eliminate the square root: (√3)^2 = (4√s - 1)^2. This simplifies to 3 = (4√s - 1)(4√s - 1).
Expand the equation: 3 = 16s - 8√s - 8√s + 1. Simplify further: 3 = 16s - 16√s + 1. Rearrange the terms: 16√s - 16s = 1 - 3, which simplifies to 16√s - 16s = -2.
Lastly, divide both sides of the equation by 16 to solve for √s: √s - s = -1/8.
Therefore, the solution to the equation is: √s = -1/8 + s.
Learn more about Solving quadratic equations involving square roots