Question

Question

Watch Video

Show Examples
Use the quadratic formula to solve. Express your answer in simplest form.
6, w, squared, minus, 26, w, plus, 5, equals, w, squared
6w
2
−26w+5=
w
2

Answer
Attempt 1 out of 5

Additional Solution
No Solution
w, equalsw=
Submit Answer
square root of, end square root
x
​

plus or minus
±

Answer 1

To solve the quadratic equation \( 6w^2 - 26w + 5 = w^2 \), we first need to move all terms to one side of the equation. We can do this by subtracting \( w^2 \) from both sides:

\[
6w^2 - 26w + 5 - w^2 = 0
\]
\[
5w^2 - 26w + 5 = 0
\]

Now, we can apply the quadratic formula, which is:

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

In our equation \( 5w^2 - 26w + 5 = 0 \), the coefficients are:
- \( a = 5 \)
- \( b = -26 \)
- \( c = 5 \)

Next, we'll calculate the discriminant \( b^2 - 4ac \):

\[
(-26)^2 - 4 \cdot 5 \cdot 5 = 676 - 100 = 576
\]

Now we can substitute into the quadratic formula:

\[
w = \frac{-(-26) \pm \sqrt{576}}{2 \cdot 5}
\]
\[
w = \frac{26 \pm 24}{10}
\]

This gives us two solutions:

1. When using the plus sign:

\[
w = \frac{26 + 24}{10} = \frac{50}{10} = 5
\]

2. When using the minus sign:

\[
w = \frac{26 - 24}{10} = \frac{2}{10} = \frac{1}{5}
\]

So the solutions for the equation \( 6w^2 - 26w + 5 = w^2 \) are:

\[
w = 5 \quad \text{and} \quad w = \frac{1}{5}
\]

In simplest form, the answers are:

\[
w = 5 \quad \text{or} \quad w = \frac{1}{5}
\]