Solving Quadratic Equations using Quadratic Formula

 Solving quadratic equations using quadratic formula

Example 1

Step 1:

 First we bring the equation in the form of ax² + bx+ c = 0.

2x² - 14 + 24 = 0

Step 2:

 then we list the coefficients a, b, and c

a = 2  b = -14 c = 14

Step 3:

 then we plug these coefficients in the formula of (-b ± √(b² - 4ac)/(2a).

x= - (-14) ± √(-14)² - 4(2)(14)

(2)(2)

Step 4:

 then, we raise -14 to the power of 2 which is 196. Then we multiply -4 with positive two and multiply the answer with positive 14. And we also multiply 2 with 2.

x = - (-14 ± √(196 - 192)

(4)

Step 5:

 then, we shall subtract 196 with 192.

x = 14 ± √(4)

   (4)

Step 6:

 after subtracting, we shall get the square root of 4.

x = 14 ± 2
       (4)

Then, we shall get the solution.

Step 7:

 first, we add 14 with positive 2 and copy the denominator. Then we divide the denominator with the answer to 14 plus positive 2. 

 
x = 14 + 2

       (4)

= 16

   4

= 4

Step 8:

 Next is, we subtract 14 with negative 2 and copy the denominator again. Then we divide the denominator with the answer to 14 minus negative 2.

x = 14 - 2       

4

= 12    
      4      

The final answers are : x = 4 and x = 3

Example 2

Step 1:

 First we bring the equation in the form of ax²+bx+c=0.

x²+2x-3=0

Step 2:

 then we list the coefficients a, b, and c

a = 1 b = 2 c = -3

Step 3:

 then we plug these coefficients in the formula of (-b) ± √(b² - 4ac)/(2a).

x= - (-2) ± √(-2)² - 4(1)(3)

(2)(1)

Step 4:

 Then, we raise -2 to the power of 2 which is 4. Then we multiply -4 with positive 1 and multiply the answer with positive 3. And we also multiply the denominator 2 with 1.

x = - (-2) ± √(4 + 12)

   (2)

Step 5: 

Then, we shall add 4 with 12.

x = -2 ± √(16)

(2)

Step 6:

 After subtracting, we shall get the square root of 16

x = - 2 ± 4

       (2)

Then, we shall get the solution.

Step 7:

 First, we add 2 with positive 4 and copy the denominator. Then we divide the denaminator with the answer to -2 plus positive 4.  

x = -2 + 4

          2  

= 2

   2

= 1

Step 8:

 Next is, we subtract -2 with negative 4 and copy the denominator again. Then we divide the denominator with the answer to -2 minus negative -4.

x = -2 - 4

        2

= 6

   3

= 2

The final answers are : x = 1 and x = 2