Use quadratic equarion to solve

Question

2x^2-7x-3=0

Answer 1

To solve the quadratic equation \(2x^2 - 7x - 3 = 0\), we can use the quadratic formula:

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

In this equation, \(a = 2\), \(b = -7\), and \(c = -3\).

First, we calculate the discriminant \(b^2 - 4ac\):

\[ b^2 - 4ac = (-7)^2 - 4 \cdot 2 \cdot (-3) \] \[ = 49 + 24 \] \[ = 73 \]

Now, we can substitute \(a\), \(b\), and the discriminant into the quadratic formula:

\[ x = \frac{-(-7) \pm \sqrt{73}}{2 \cdot 2} \] \[ = \frac{7 \pm \sqrt{73}}{4} \]

So, the two solutions for \(x\) are:

\[ x_1 = \frac{7 + \sqrt{73}}{4} \] \[ x_2 = \frac{7 - \sqrt{73}}{4} \]

These are the solutions to the equation \(2x^2 - 7x - 3 = 0\).

Answer 2

So whats the answer to x=

Answer 3

The solutions to the equation \(2x^2 - 7x - 3 = 0\) are:

\[ x_1 = \frac{7 + \sqrt{73}}{4} \]

\[ x_2 = \frac{7 - \sqrt{73}}{4} \]

To give numerical approximations:

1. Calculating \(x_1\):

   \[ x_1 \approx \frac{7 + 8.544}{4} \approx \frac{15.544}{4} \approx 3.886 \]

2. Calculating \(x_2\):

   \[ x_2 \approx \frac{7 - 8.544}{4} \approx \frac{-1.544}{4} \approx -0.386 \]

Thus, the approximate solutions are:

\[ x_1 \approx 3.886 \]

\[ x_2 \approx -0.386 \]

You can use these values as the solutions for \(x\).

Answer 4

I dont need yucky decimals I need one good concerte answer

Answer 5

Got it! The solutions to the equation \(2x^2 - 7x - 3 = 0\) in their exact form are:

\[ x = \frac{7 + \sqrt{73}}{4} \quad \text{and} \quad x = \frac{7 - \sqrt{73}}{4} \]

If you prefer a single concise answer, you can indicate that the equation has two solutions:

\[ x = \frac{7 \pm \sqrt{73}}{4} \]

This represents both solutions without using decimals.