Final answer:
To find the solutions to the equation, isolate the variable x. Solve step by step using the quadratic formula. The smaller solution is x = 0.417 and the larger solution is x = 1.042.
Step-by-step explanation:
To find the solutions to the equation √(1x+1) + 4 = 6x, we need to isolate the variable x. Let's solve it step by step:
- Subtract 4 from both sides of the equation: √(1x+1) = 6x - 4
- Square both sides to eliminate the square root: (1x+1) = (6x - 4)^2
- Expand and simplify: x+1 = 36x^2 - 48x + 16
- Rearrange terms: 36x^2 - 49x + 15 = 0
- Use the quadratic formula to find the values of x: x = (-b ± √(b^2 - 4ac))/(2a)
- Plug in the values a = 36, b = -49, and c = 15 into the formula and solve it.
After solving the equation, we find that the smaller possible solution is x = 0.417 and the larger possible solution is x = 1.042. To check if these solutions are correct, substitute them back into the original equation and see if both sides are equal.