*x*2+*x*29​=10, let's start by multiplying both sides of the equation by x2*x*2 to get rid of the fraction. This gives us x4+9=10x2*x*4+9=10*x*2.

It seems there are a few issues in the equation as written, and I believe you're attempting to solve a quadratic equation but have mixed terms. Let's clarify the equation first, and then I'll help you solve it.

You might have meant:

\[
x^2 + \frac{29}{x^2} = 10
\]

This is a nonlinear equation involving \(x^2\), and solving it requires multiplying by \(x^2\) to clear the fraction. Let me break it down step-by-step:

### Step 1: Multiply both sides by \(x^2\)
Multiply both sides of the equation by \(x^2\) to eliminate the fraction:

\[
x^4 + 29 = 10x^2
\]

### Step 2: Rearrange the equation
Rearrange the equation to bring all terms to one side:

\[
x^4 - 10x^2 + 29 = 0
\]

### Step 3: Use substitution
To solve this quartic equation, we can substitute \(y = x^2\), which turns it into a quadratic equation:

\[
y^2 - 10y + 29 = 0
\]

### Step 4: Solve the quadratic equation
Now solve the quadratic equation using the quadratic formula:

\[
y = \frac{-(-10) \pm \sqrt{(-10)^2 - 4(1)(29)}}{2(1)}
\]
\[
y = \frac{10 \pm \sqrt{100 - 116}}{2}
\]
\[
y = \frac{10 \pm \sqrt{-16}}{2}
\]
\[
y = \frac{10 \pm 4i}{2}
\]
\[
y = 5 \pm 2i
\]

### Step 5: Substitute back \(y = x^2\)
Since \(y = x^2\), we now have:

\[
x^2 = 5 + 2i \quad \text{or} \quad x^2 = 5 - 2i
\]

Taking square roots gives us the complex solutions for \(x\). To summarize:

\[
x = \pm \sqrt{5 + 2i} \quad \text{or} \quad x = \pm \sqrt{5 - 2i}
\]

### Conclusion
The equation has complex solutions.

Do you want more details on solving for the square roots of complex numbers, or any other specific questions?

Here are 5 related questions:
1. How do you find the square root of a complex number?
2. Can we solve quartic equations without substitution?
3. What are the properties of complex numbers and their square roots?
4. Are there real solutions to this equation, or only complex ones?
5. How does the quadratic formula work with complex discriminants?

**Tip**: When solving quartic equations, substitution is a common trick to reduce the equation to a simpler quadratic form.

The query submitted by the user: *x*^2 + *x*29 = 10. Let's start by multiplying both sides of the equation by x^2 to get rid of the fraction. This gives us x^4 + 9 = 10x^2.

This tutorial walks through solving a quartic equation x^4 - 10x^2 + 29 = 0 using substitution and the quadratic formula. The solution involves complex numbers, making it ideal for students in Grades 10-12 interested in advanced algebra concepts.

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