https://file.aiquickdraw.com/mathbot/file/1725931917675cq58cpka.jpg

The equation in the image is:

\[ 21w^2 - 5w - 26 = -8 \]

First, let's simplify the equation by moving all terms to one side:

\[ 21w^2 - 5w - 26 + 8 = 0 \]
\[ 21w^2 - 5w - 18 = 0 \]

We will now solve this quadratic equation for \(w\). We can use the quadratic formula:

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

where \(a = 21\), \(b = -5\), and \(c = -18\). Let's calculate the solutions.The solutions to the equation \( 21w^2 - 5w - 18 = 0 \) are:

\[ w = \frac{5 - \sqrt{1537}}{42} \] and \[ w = \frac{5 + \sqrt{1537}}{42} \]

These solutions are in their exact form involving a square root.

Would you like more details or have any questions about these steps?

Here are some additional questions that might help you explore further:
1. What happens if we try to factorize this quadratic equation manually?
2. How can we verify these solutions are correct?
3. What is the discriminant of this quadratic equation and what does it tell us about the nature of the roots?
4. How would the solutions change if the coefficient of \( w^2 \) were different?
5. Can we graph this equation to visually confirm the locations of the roots?

**Tip:** When using the quadratic formula, it’s important to pay close attention to the signs of the coefficients, as they directly affect the calculation of the discriminant and the resulting solutions.

Solve the quadratic equation: 2w^2 - 5w - 26 = -8.

Learn how to solve the quadratic equation 2w^2 - 5w - 26 = -8 by simplifying the equation and using the quadratic formula. Understand key concepts like discriminants and how they determine the nature of the roots. Suitable for high school students (Grades 9-12).

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