Question

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

Answer 1

ANSWER

$x=1.39$ to the nearest hundredth.

EXPLANATION

We have the equation,

$0=2x^2+3x-8$

Which can be rewritten as

$2x^2+3x-8=0$

The question demands the use of the quadratic formula.

Comparing this to the general quadratic equation;

$ax^2+bx+c=0$

$a=2,b=3,c=-8$

The quadratic formula is given by;

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

We now substitute all the values in to the formula;

$x=\frac{-3\pm\sqrt{(3)^2-4(2)(-8)}}{2(2)}$

We simplify to obtain;

$x=\frac{-3\pm\sqrt{9+64}}{4}$

$x=\frac{-3\pm\sqrt{73}}{4}$

We now split the plus or minus sign to obtain;

$x=\frac{-3-\sqrt{73}}{4}$

This implies that;

$x=-2.89$

Or

$x=\frac{-3+\sqrt{73}}{4}$

This will evaluate to;

$x=1.39$

Hence, the positive solution rounded to the nearest hundredth is

$x \approx 1.39$

Answer 2

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