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Answer :
- Isolate the square root term: $\sqrt{x+59} = 20 - 12 = 8$.
- Square both sides: $x+59 = 8^2 = 64$.
- Isolate $x$: $x = 64 - 59 = 5$.
- The solution is $\boxed{5}$.
### Explanation
1. Isolating the Square Root
We are given the equation $\sqrt{x+59}+12=20$ and we want to solve for $x$. Our first goal is to isolate the square root term.
2. Simplifying the Equation
Subtract 12 from both sides of the equation to isolate the square root:$$\sqrt{x+59} + 12 - 12 = 20 - 12$$$$\sqrt{x+59} = 8$$
3. Eliminating the Square Root
Now that we have isolated the square root, we can eliminate it by squaring both sides of the equation:$$(\sqrt{x+59})^2 = 8^2$$$$x+59 = 64$$
4. Isolating x
To solve for $x$, we need to isolate it by subtracting 59 from both sides of the equation:$$x + 59 - 59 = 64 - 59$$$$x = 5$$
5. Final Answer
Therefore, the solution to the equation is $x=5$.
### Examples
Imagine you are designing a garden and need to determine the length of one side of a square flower bed. If the area of the flower bed plus an additional 59 square feet needs to be such that the square root of the total area is 8 feet less than 20 feet, this problem helps you find the exact length needed for the flower bed's side. This type of problem applies to various scenarios involving area calculations and geometric design.
- Square both sides: $x+59 = 8^2 = 64$.
- Isolate $x$: $x = 64 - 59 = 5$.
- The solution is $\boxed{5}$.
### Explanation
1. Isolating the Square Root
We are given the equation $\sqrt{x+59}+12=20$ and we want to solve for $x$. Our first goal is to isolate the square root term.
2. Simplifying the Equation
Subtract 12 from both sides of the equation to isolate the square root:$$\sqrt{x+59} + 12 - 12 = 20 - 12$$$$\sqrt{x+59} = 8$$
3. Eliminating the Square Root
Now that we have isolated the square root, we can eliminate it by squaring both sides of the equation:$$(\sqrt{x+59})^2 = 8^2$$$$x+59 = 64$$
4. Isolating x
To solve for $x$, we need to isolate it by subtracting 59 from both sides of the equation:$$x + 59 - 59 = 64 - 59$$$$x = 5$$
5. Final Answer
Therefore, the solution to the equation is $x=5$.
### Examples
Imagine you are designing a garden and need to determine the length of one side of a square flower bed. If the area of the flower bed plus an additional 59 square feet needs to be such that the square root of the total area is 8 feet less than 20 feet, this problem helps you find the exact length needed for the flower bed's side. This type of problem applies to various scenarios involving area calculations and geometric design.
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