1

Problem

Solved for non-linear equations \$7x^2 = 5x + 12\$.

2

Step

The given equation is written as

\$7x^2 - 5x - 12 = 0\$

3

Step

Applying the factorization technique:

\$7x^2 -12x +7x -12 =0\$

\$x(7x -12) + 1 (7x-12) = 0\$

\$(7x -12) (x +1) = 0\$

4

Step

Finding x values:

7x - 12 = 0 and x + 1 = 0

\$x = (12)/7\$ and x = - 1

5

Solution

Therefore, the solutions to the equation is \$7x^2 = 5x + 12\$ are \$x = (12)/7\$ and x = - 1.

6

Sumup

Please summarize steps

Choices

7

Choice-A

This option correctly includes both solutions we found: \$x = (12)/7\$ and x = −1. Therefore, Option A is correct

Correct \$x = (12)/7\$ and x = -1

8

Choice-B

The answer is incorrect; It’s the inverse of the right answer with a negative sign

Wrong \$x = - 7/(12)\$ and x = -1

9

Choice-C

The answer is wrong; The right one has a positive sign, while this choice has a negative sign

Wrong \$x = -(12)/7\$ and x = -1

10

Choice-D

Option D’s inaccuracy lies in proposing \$x = 7/(12)\$ instead of the correct \$x = (12)/7\$ as in option A

Wrong \$x = 7/(12)\$ and x = -1

11

Answer

Option

A

12

Sumup

Please summarize choices