# Solving Quadratic Equations / Prime Number Formula

Solving Quadratic Equations / Prime Number Formula

Project 1:   An interesting method for solving quadratic equations came from India.   I will provide you the necessary steps to solve the quadratic equation.   Then I will have four examples that will show the formula in use.
Step 1 – Move the constant term to the right side of the equation.
Step 2 – Multiply each term in the equation by four times the coefficient of the x2 term.
Step 3 – Square the coefficient of the original x term and add it to both sides of the equation.
Step 4 – Take the square root of both sides.
Step 5 – Set the left side of the equation equal to the positive square root of the number on the right side and solve for x.
Step 6 – Set the left side of the equation equal to the negative square root of the number on the   right side of the equation and solve for x.

(a) First example:
x2 – 2x – 13 = 0
(Step 1) x2 – 2x – 13 + 13 = 0 + 13
x2 – 2x = 13
(Step 2)                   4x2 – 8x = 52
(Step 3)             4x2 – 8x + 4 = 52 + 4
4x2 – 8x + 4 = 56
(Step 4)                       2x – 2 = + 7.48
(Step 5) (Step 6)
2x – 2 = 7.48 | 2x – 2 = - 7.48
+ 2     + 2   |                 + 2       + 2
|
2x = 9.48 |       2x = - 5.48
2         2 |       2       2
|
x = 4.74 |         x = - 2.74

(b) Second example:
4x2 – 4x + 3 = 0
(Step 1)     4x2 – 4x + 3 - 3 = 0 - 3
4x2 – 4x = - 3
(Step 2)                   64x2 – 64x = - 48
(Step 3)           64x2 – 64x + 16 = - 48 + 16
16(2x – 1)2   = - 32
(Step 4)                   4(2x – 1)2   = + - 4i
(Step 5) (Step 6)
2x – 2 = i | 2x – 2 = - i
+ 2   + 2   |                 + 2       + 2
|
2x = i |       2x = - i...