1

Problem

Solve the quadratic equation: \$3x^2 - 4x - 4 = 0 \$.

2

Step

The given

\$3x^2 - 4x - 4 = 0 \$

3

Formula

The quadratic formula states that for an equation of the form \$ax^2 + bx + c = 0\$, the solutions for x can be found using the formula: \$x = (-b ± \sqrt(b^2 - 4ac)) / (2a) \$

4

Hint

Here: a = 3, b = - 4 , c= -4.

5

Step

Plug the values in the formula:

\$ x = (-(-4) ± \sqrt((-4)^2 - 4 \times 3 \times -4)) / (2 \times 3) \$

\$ x = (4 ± 8) / 6 \$

6

Step

When we take the positive and negative square roots then simplified:

\$ x = (4 + 8) / 6 \$ and \$ x = (4 - 8) / 6 \$

\$ x = \cancel12^2 / \cancel6^1 \$ and \$ x = - \cancel4^2 / \cancel6^3 \$

x = 2 and \$ x = - 2/3 \$

7

Solution

Therefore, the solutions to the equation \$3x^2 - 4x - 4 = 0\$ are x = 2 and \$x = -2/3\$.

8

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

9

Choice-A

The solutions provided for the quadratic equations are inaccurate and do not represent a valid solution

Wrong \$ x = 2 or x = 3/2 \$

10

Choice-B

The solutions provided for the quadratic equations are inaccurate and do not represent a valid solution

Wrong \$ x = - 2 or x = - 2/3 \$

11

Choice-C

The solutions provided for the quadratic equations are inaccurate and do not represent a valid solution

Wrong \$ x = - 2 or x = - 3/2 \$

12

Choice-D

Both solutions of the quadratic equation are correct and valid

Correct \$ x = 2 or x = - 2/3 \$

13

Answer

Option

D

14

Sumup

Please summarize choices