Questions: Solve using the quadratic formula. -5s^2+8s+5=0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. s= or s=

Solution Steps

To solve the quadratic equation \(-5s^2 + 8s + 5 = 0\) using the quadratic formula, we identify the coefficients \(a = -5\), \(b = 8\), and \(c = 5\). The quadratic formula is given by:

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

We will calculate the discriminant \(b^2 - 4ac\) and then use it to find the two possible values for \(s\).

For the quadratic equation \(-5s^2 + 8s + 5 = 0\), we identify the coefficients: \[ a = -5, \quad b = 8, \quad c = 5 \]

We calculate the discriminant using the formula \(D = b^2 - 4ac\): \[ D = 8^2 - 4(-5)(5) = 64 + 100 = 164 \]

Using the quadratic formula \(s = \frac{-b \pm \sqrt{D}}{2a}\), we find the two solutions: \[ s_1 = \frac{-8 + \sqrt{164}}{2(-5)} \quad \text{and} \quad s_2 = \frac{-8 - \sqrt{164}}{2(-5)} \]

Calculating the values: \[ s_1 = \frac{-8 + \sqrt{164}}{-10} \approx -0.48 \] \[ s_2 = \frac{-8 - \sqrt{164}}{-10} \approx 2.08 \]

Final Answer