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can the answer for this equation just be written solely as x=4, or do i have to write 'x=4, x=4'

The quadratic equation shown in the image is:

\[
x^2 - 5x + 16 = 2 + 3x
\]

This simplifies to:

\[
x^2 - 5x + 16 - 2 - 3x = 0
\]

\[
x^2 - 8x + 14 = 0
\]

From there, it's factored as \((x - 4)(x - 4) = 0\), which gives:

\[
x - 4 = 0
\]

So, the solution is \(x = 4\).

Since both roots are the same, you do not need to write "x = 4, x = 4." The correct and concise way to express the solution is simply \(x = 4\).

Would you like any more details, or do you have any other questions?

Here are some related questions:

1. How can you verify that \(x = 4\) is the correct solution to the equation?
2. What is the significance of a quadratic equation having a double root?
3. How would you express the solution if the roots were distinct?
4. What methods can be used to solve quadratic equations other than factoring?
5. Can the quadratic formula be used to solve this equation? If so, how?
6. How would you graph the function \(f(x) = x^2 - 8x + 14\)?
7. What does the discriminant tell you about the roots of a quadratic equation?
8. How can completing the square be applied to solve the equation?

**Tip:** When solving quadratic equations, always check if the equation can be factored easily before using other methods like the quadratic formula.

Explore the solution to the quadratic equation x^2 - 8x + 14 with detailed steps and explanations. Learn about factoring quadratic equations and the significance of double roots. Suitable for high school students studying algebra and quadratic equations.

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