To solve the quadratic equation \(5y^2 − 8y = 2\) using the quadratic formula, we start by rewriting it in the standard form \(ay^2 + by + c = 0\).
First, subtract 2 from both sides of the equation:
\[5y^2 - 8y - 2 = 0\]
Here, \(a = 5\), \(b = -8\), and \(c = -2\).
The quadratic formula is given by:
\[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Plugging in the values of \(a\), \(b\), and \(c\), we get:
\[ y = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(5)(-2)}}{2(5)} \]
Simplify the expression:
\[ y = \frac{8 \pm \sqrt{64 + 40}}{10} \]
\[ y = \frac{8 \pm \sqrt{104}}{10} \]
The square root of 104 can be simplified further:
\[ \sqrt{104} \approx 10.20 \] (to the nearest hundredth)
Now we have:
\[ y = \frac{8 \pm 10.20}{10} \]
This gives us two possible solutions:
\[ y_1 = \frac{8 + 10.20}{10} = \frac{18.20}{10} = 1.82 \]
\[ y_2 = \frac{8 - 10.20}{10} = \frac{-2.20}{10} = -0.22 \]
Therefore, the solutions to the equation \(5y^2 - 8y = 2\) are approximately:
\[ y = 1.82, \, -0.22 \]
Thus, the correct answer is:
\[ 1.82, -0.22 \]
13.
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
5y2 − 8y = 2
0.22, –1.82
11.2, –9.6
3.64, –0.44
1.82, –0.22
1 answer