Rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0 = 2x2 + 3x – 8? quadratic formula: x =

The answer is x = 1.39 or -2.89.

Explanation:

The quadratic formula is  x = -b+/-√(b²-4ac)/2a.

Although I usually use other methods to solve quadratics, I can use the quadratic formula.

First, you have to know the different parts of a quadratic:  ax² + bx + c = 0.  Since your equation is 2x² + 3x - 8 = 0, we know that:

a = 2
b = 3
c = -8

Now, all we need to do is plug these values into the quadratic formula and solve.

x = -3+/-√(3²-4·2·(-8))/2·2.

Next, we can simplify this to x = -3+/-√(73)/4.

Normally, I would leave the answer as this, because √73 is an irrational number, and this is in simplest radical form, but the question instructs us to round to the nearest hundredth, indicating that further work is necessary.

We need to square root 73, which is approximately 8.54.  You should now have  x = (-3+/-8.54)/4.

From here, we need to calculate the answer when it is positive 8.54 and when it is negative 8.54.

x = (-3+8.54)/4 ⇒ x = 5.54/4 ⇒ x = 1.385 ⇒ x = 1.39  (because it says to round to the hundredths)

x = (-3-8.54)/4 ⇒ x = -11.54/4 ⇒ x = -2.885 ⇒ x = -2.89

x = 1.39 or -2.89

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