The 4 real solutions is correct, sure, but are these the correct 4 solutions? Can you count the X to the power of 2 solutions as 'real'? because I was thinking that the 4 real solutions are: - radical 1.3, + radical 1.3, - radical 0.175 and + radical 0.175. If the test wanted me to write the 4 real solutions, wouldn't these 4 be the correct ones?

To determine if the given solutions are correct, let's clarify the following concepts:

1. **Real Solutions:** Real solutions of an equation are the values of the variable that satisfy the equation and are real numbers (not imaginary).
2. **Square Roots:** When solving equations involving squares, the solutions can be both positive and negative roots.

Given the context, it seems you are referring to an equation that has been solved to yield four roots involving square roots. Let's examine the potential solutions you provided:

- \( -\sqrt{1.3} \)
- \( +\sqrt{1.3} \)
- \( -\sqrt{0.175} \)
- \( +\sqrt{0.175} \)

These are indeed real solutions because the square roots of positive numbers are real, and considering both the positive and negative roots is standard practice.

To see if these are the solutions to a quadratic equation, let’s consider the form of the equation that would yield such solutions. For instance, if we have a quadratic equation in the form:
\[ ax^2 + bx + c = 0 \]

The solutions for this equation can be found using the quadratic formula:
\[ x = \frac{-b \

Explore the concept of real solutions and square roots in quadratic equations with a detailed explanation. Learn how to identify and interpret solutions involving square roots. Suitable for high school students studying algebra.

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