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We are given the quadratic equation \( 2x^2 + 20x - 70 = 0 \), and we need to find an equivalent equation by completing the square.

### Steps for Completing the Square:

1. **Divide the equation by the leading coefficient** (2 in this case) to make the coefficient of \( x^2 \) equal to 1:
   \[
   \frac{2x^2 + 20x - 70}{2} = \frac{0}{2}
   \]
   This simplifies to:
   \[
   x^2 + 10x - 35 = 0
   \]

2. **Move the constant term to the other side**:
   \[
   x^2 + 10x = 35
   \]

3. **Complete the square** by adding \( \left(\frac{10}{2}\right)^2 = 25 \) to both sides:
   \[
   x^2 + 10x + 25 = 35 + 25
   \]
   This simplifies to:
   \[
   (x + 5)^2 = 60
   \]

The equation equivalent to \( 2x^2 + 20x - 70 = 0 \) by completing the square is \( (x + 5)^2 = 60 \).

Thus, the correct answer is:
\[
\boxed{(x + 5)^2 = 60}
\]

Would you like further explanation on this method? Here are five related questions:

1. How do you complete the square when the leading coefficient isn't 1?
2. Can completing the square be used to solve all quadratic equations?
3. How do you factor a quadratic expression after completing the square?
4. What is the significance of the vertex form obtained through completing the square?
5. How does completing the square relate to solving quadratic equations using the quadratic formula?

**Tip:** When completing the square, always ensure the coefficient of \(x^2\) is 1 before adding a number to both sides.

Which equation is equivalent to 2x^2 + 20x - 70 = 0 by completing the square?

Learn how to solve the quadratic equation 2x^2 + 20x - 70 = 0 by completing the square. This problem demonstrates key concepts in algebra, including completing the square and transforming the equation to vertex form. Suitable for students in Grades 8-10.

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