To solve the quadratic equation \(a^2 - 2a - 224 = 0\) using the quadratic formula, we will follow these steps:
The quadratic formula is given by:
\[ a = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
For the equation \(a^2 - 2a - 224 = 0\), we identify the coefficients as follows:
- \(a = 1\)
- \(b = -2\)
- \(c = -224\)
Now we plug these values into the quadratic formula:
\[ a = \frac{-(-2) \pm \sqrt{(-2)^2 - 4 \cdot 1 \cdot (-224)}}{2 \cdot 1} \]
Simplifying inside the square root:
\[ a = \frac{2 \pm \sqrt{4 + 896}}{2} \]
\[ a = \frac{2 \pm \sqrt{900}}{2} \]
We know that \(\sqrt{900} = 30\), so:
\[ a = \frac{2 \pm 30}{2} \]
This gives us two solutions:
1. When we take the positive root:
\[ a = \frac{2 + 30}{2} = \frac{32}{2} = 16 \]
2. When we take the negative root:
\[ a = \frac{2 - 30}{2} = \frac{-28}{2} = -14 \]
So the solutions are \( a = 16 \) and \( a = -14 \).
Thus, the correct answer is:
\[ \boxed{16, -14} \]
3.
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
a2 − 2a − 224 = 0
8, –28
–8, 28
16, –14
–16, 14
1 answer
4 answers