1

Problem

Solve the nonlinear equation: \$ x^2 - 5x + 6 = 0 \$.

2

Step

The given nonlinear equation is

\$x^2 - 5x + 6 = 0\$

3

Step

Utilizing factorization method:

\$ x^2 - 3x - 2x + 6 = 0 \$

\$ x(x - 2) - 3(x - 2) = 0 \$

\$ (x - 2)(x - 3) = 0 \$

4

Step

Find for x values:

\$x - 2 = 0 and x - 3 = 0 \$

\$x = 2 and x = 3 \$

5

Solution

Therefore, the solutions to the equation \$x^2 - 5x + 6 = 0\$ are \$ x = 2 and x = 3 \$.

6

Sumup

Please summarize steps

Choices

7

Choice-A

This option is accurate since it validates both x = 2 and x = 3 as solutions to the given equation

Correct x = 2 and x = 3

8

Choice-B

At x = -1 and x = 4, the original equation isn’t satisfied, making option B incorrect

Wrong x = -1 and x = 4

9

Choice-C

The equation isn’t satisfied by x = - 2 and x = 5, so they’re not valid solutions for the given equation

Wrong x = - 2 and x = 5

10

Choice-D

Option D incorrectly labels one solution as x = - 2 instead of correctly x = 2

Wrong x = 3 and x = - 2

11

Answer

Option

A

12

Sumup

Please summarize choices