$$ Solve\,the\,quadratic\,\,equation.\,\,\,\,\,\,28x^2-x-2=0 $$$$ \text{  } $$The field below accepts a list of numbers or formulas separated by semicolons ( e.g. 2; 4; 6 or $$ x+1;\text{ }x-1 $$

To solve the quadratic equation $ 28x^2 - x - 2 = 0 $, we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Where:
- $ a = 28 $
- $ b = -1 $
- $ c = -2 $

Now, substitute the values into the formula:

\[
x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(28)(-2)}}{2(28)}
\]

Simplify:

\[
x = \frac{1 \pm \sqrt{1 + 224}}{56}
\]

\[
x = \frac{1 \pm \sqrt{225}}{56}
\]

\[
x = \frac{1 \pm 15}{56}
\]

Now, solving for the two cases:
1. $ x = \frac{1 + 15}{56} = \frac{16}{56} = \frac{2}{7} $
2. $ x = \frac{1 - 15}{56} = \frac{-14}{56} = \frac{-1}{4} $

Thus, the solutions are:

\[
x = \frac{2}{7}; \, x = \frac{-1}{4}
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do you derive the discriminant in the quadratic formula?
2. What are the conditions for a quadratic equation to have real roots?
3. Can the quadratic formula be used for non-integer coefficients?
4. How do you factor quadratic equations without the quadratic formula?
5. What is the relationship between the discriminant and the nature of the roots?

**Tip:** Always check the discriminant ($b^2 - 4ac$) first to determine the type of roots!

Solve the quadratic equation: 28x^2 - x - 2 = 0. The field below accepts a list of numbers or formulas separated by semicolons (e.g., 2; 4; 6 or x+1; x-1).

Learn how to solve the quadratic equation 28x^2 - x - 2 = 0 using the quadratic formula. This solution provides a step-by-step explanation, including key algebraic concepts, the quadratic equation formula, and application of the quadratic formula theorem. Suitable for students in Grades 9-12.

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