Solve step by step x^2+y+23 = sqrt(3456567890)

To solve the equation \(x^2 + y + 23 = \sqrt{3,456,567,890}\), we'll proceed step by step.

### Step 1: Simplify the Square Root
First, let's calculate the value of \(\sqrt{3,456,567,890}\):

\[
\sqrt{3,456,567,890} \approx 58,793.67
\]

So, the equation becomes:

\[
x^2 + y + 23 = 58,793.67
\]

### Step 2: Isolate the Terms Involving \(x\) and \(y\)
Next, subtract 23 from both sides to isolate the terms with \(x\) and \(y\):

\[
x^2 + y = 58,793.67 - 23
\]

Simplifying the right side:

\[
x^2 + y = 58,770.67
\]

### Step 3: Express \(y\) in Terms of \(x\)
To express \(y\) in terms of \(x\), subtract \(x^2\) from both sides:

\[
y = 58,770.67 - x^2
\]

### Summary
The equation \(x^2 + y + 23 = \sqrt{3,456,567,890}\) simplifies to \(y = 58,770.67 - x^2\). This is the solution expressed in terms of \(x\).

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. How do you solve quadratic equations when given a specific value for \(y\)?
2. What is the significance of the square root in the original equation?
3. How would you graph the equation \(y = 58,770.67 - x^2\)?
4. What happens to the value of \(y\) as \(x\) increases or decreases?
5. How can you check if the solution is correct?

**Tip:** When solving equations, always simplify square roots or other operations as early as possible to make the equation easier to work with.

Learn how to solve the equation x^2 + y + 23 = sqrt(3456567890) step by step with a detailed mathematical solution. This problem involves algebraic manipulation, including simplifying square roots and isolating variables. Suitable for advanced high school students.

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