Which equation has the same solution as x, squared, minus, 20, x, plus, 14, equals, 4x
2
−20x+14=4?

The given equation is:

\[
x^2 - 20x + 14 = 4
\]

To find an equivalent equation, let's solve it step by step.

### Step 1: Subtract 4 from both sides to set the equation equal to 0:
\[
x^2 - 20x + 14 - 4 = 0
\]
Simplifying:
\[
x^2 - 20x + 10 = 0
\]

This quadratic equation has the same solutions as the original equation. So, the equation with the same solution is:

\[
x^2 - 20x + 10 = 0
\]

### Would you like me to explain how to solve this equation or provide further details on the solution?

Here are 5 related questions to explore further:
1. How do you factor a quadratic equation like \( x^2 - 20x + 10 = 0 \)?
2. Can you use the quadratic formula to solve \( x^2 - 20x + 10 = 0 \)?
3. What is the discriminant of the quadratic equation \( x^2 - 20x + 10 = 0 \)?
4. What are the steps to complete the square for this equation?
5. How does graphing \( x^2 - 20x + 10 = 0 \) help visualize the solution?

**Tip**: When solving quadratic equations, always try factoring first, then the quadratic formula if necessary.

Which equation has the same solution as x^2 - 20x + 14 = 4?

Explore how to solve the quadratic equation x^2 - 20x + 14 = 4 by simplifying and transforming it to the form x^2 - 20x + 10 = 0. Learn step-by-step methods, including factoring and using the quadratic formula, tailored for students in Grades 8-10.

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