1

Problem

Solve the quadratic equation \$2x^2 + x − 4 = 0\$ by completing the square.

2

Step

Rearrange the equation by shifting the constant term (- 4) to the opposite side

\$2x^2 + x = 4\$

3

Step

Divide the entire equation by the coefficient of \$x^2\$ to ensure the leading coefficient becomes 1

\$x^2 + 1/2 x = 2\$

4

Step

Take half of the coefficient of the x term, square it, and add it to both sides of the equation:

\$x^2 + 2 (1/4) x + 1/(16) = 2 + 1/(16)\$

5

Step

Square the left side of the equation and express it as a perfect square by factoring

\$(x + 1/4)^2 = (33)/(16)\$

6

Step

Solve for x by finding the square root of each side

\$x + 1/4 = ± \sqrt(33)/4\$

⇒x = \$−1/4\$ ± \$\sqrt(33)/4\$

7

Solution

Hence, completing the square for the quadratic equation \$2x^2 + x − 4 = 0\$ yields solutions: x = \$((-1) + \sqrt(33))/4\$ and x = \$((−1) − \sqrt(33))/4\$.

8

Sumup

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

Choices

9

Choice-A

This option is incorrect because solutions given for the quadratic equation are not applicable

Wrong x = \$((−1) + \sqrt(33))/2\$ and x = \$((−1) − \sqrt(33))/2\$

10

Choice-B

This option is incorrect because the solutions provided for the quadratic equation are not applicable.

Wrong x = \$((1) + \sqrt(33))/2\$ and x = \$((1) − \sqrt(33))/2\$

11

Choice-C

This option is incorrect because solutions given for the quadratic equation are not applicable

Wrong x = \$((1) + \sqrt(33))/4\$ and x = \$((1) − \sqrt(33))/4\$

12

Choice-D

This option is correct because the pair of solutions aligns with the provided quadratic equation

Correct x = \$((-1) + \sqrt(33))/4\$ and x = \$((-1) − \sqrt(33))/4\$

13

Answer

Option

D

14

Sumup

Please summarize choices