Solve the expression (5 + √(x - 5)) = 5
Understand the Problem
The question appears to involve solving a mathematical expression that includes a square root, indicated by the presence of a radical symbol in the image. The necessary steps will involve simplifying the expression inside the square root and potentially solving for a variable if it is part of the equation.
Answer
The final answer is $x = 5$.
Answer for screen readers
The final answer is $x = 5$.
Steps to Solve
- Isolate the square root
Start with the equation given:
$$(5 + \sqrt{x - 5}) = 5$$
Subtract 5 from both sides to isolate the square root:
$$\sqrt{x - 5} = 5 - 5$$
This simplifies to:
$$\sqrt{x - 5} = 0$$
- Square both sides to eliminate the square root
Now, square both sides to eliminate the square root:
$$(\sqrt{x - 5})^2 = 0^2$$
This simplifies to:
$$x - 5 = 0$$
- Solve for x
To find the value of $x$, add 5 to both sides:
$$x = 5$$
The final answer is $x = 5$.
More Information
The equation involves using square roots and isolating variables. The square root of zero is zero, which leads to a straightforward solution. It’s essential to verify that the solution satisfies the original equation.
Tips
- Failing to isolate the square root first, which can lead to incorrect simplifications.
- Forgetting to square both sides properly, leading to missing possible solutions.
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