Final answer:
The solution to √(8x) = 4 + 2x involves first squaring both sides and simplifying, but the resulting quadratic equation has no real solutions, indicating a potential typo in the given equation.
Step-by-step explanation:
To solve the equation √(8x) = 4 + 2x, we first square both sides to remove the square root, yielding:
8x = (4 + 2x)²
Now, expand the right side of the equation:
8x = 16 + 16x + 4x²
To solve the quadratic equation, collect all terms on one side:
4x² + 16x - 8x + 16 = 0
Combining like terms, we have:
4x² + 8x + 16 = 0
Dividing the entire equation by 4 simplifies it:
x² + 2x + 4 = 0
This is a quadratic equation, and it seems that there might have been a typo as this particular quadratic equation has no real solutions. Therefore, if we were solving √(8x) = 4 + 2x, it is likely that the actual equation was different. If it were √(8x) = 4 - 2x, squaring both sides would lead to:
8x = (4 - 2x)²
8x = 16 - 16x + 4x²
4x² + 16x - 8x - 16 = 0
4x² + 8x - 16 = 0
x² + 2x - 4 = 0
Now, using the quadratic formula, we find that the equation does have real solutions, unlike our previous case. Always double-check the initial equation for typos.