X+6 ___ 2x+ 1

X + 3
___
2x - 1

x=  

11

​  

+1

x=1−  

11

​  

Step-by-step explanation:

(x+3)⋅(x−3)=2x+1

Consider (x+3)(x−3). Multiplication can be transformed into difference of squares using the rule: (a−b)(a+b)=a  

2

−b  

2

. Square 3.

x  

2

−9=2x+1

Subtract 2x from both sides.

x  

2

−9−2x=1

Subtract 1 from both sides.

x  

2

−9−2x−1=0

Subtract 1 from −9 to get −10.

x  

2

−10−2x=0

All equations of the form ax  

2

+bx+c=0 can be solved using the quadratic formula:  

2a

−b±  

b  

2

−4ac

​  

​  

. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x  

2

−2x−10=0

This equation is in standard form: ax  

2

+bx+c=0. Substitute 1 for a, −2 for b, and −10 for c in the quadratic formula,  

2a

−b±  

b  

2

−4ac

​  

​  

.

x=  

2

−(−2)±  

(−2)  

2

−4(−10)

​  

​  

Square −2.

x=  

2

−(−2)±  

4−4(−10)

​  

​  

Multiply −4 times −10.

x=  

2

−(−2)±  

4+40

​  

​  

Add 4 to 40.

x=  

2

−(−2)±  

44

​  

​  

Take the square root of 44.

x=  

2

−(−2)±2  

11

​  

​  

The opposite of −2 is 2.

x=  

2

2±2  

11

​  

​  

Now solve the equation x=  

2

2±2  

11

​  

​  

 when ± is plus. Add 2 to 2  

11

​  

.

x=  

2

2  

11

​  

+2

​  

Divide 2+2  

11

​  

 by 2.

x=  

11

​  

+1

Now solve the equation x=  

2

2±2  

11

​  

​  

 when ± is minus. Subtract 2  

11

​  

 from 2.

x=  

2

2−2  

11

​  

​  

Divide 2−2  

11

​  

 by 2.

x=1−  

11

​  

The equation is now solved.

x=  

11

​  

+1

x=1−  

11

​  

"if it is my birthday, then it is snowing"

step-by-step explanation: