How To Simplify Quadratic Equations?

How to simplify quadratic equations?

 

Answer:

You can use three ways:

▪ Completing the Square

▪By Factoring

▪Using the formula⬆

Factoring:

▪Combine all of the like terms and move them to one side of the equation.

2x^2-8x-4=3x-x^2 ➡ 2x^2 + x^2 - 8x -3x -4 = 0 ➡ 3x^2 - 11x -4=0

▪Factor the expression.

3x^2 - 11x -4=0 ➡ (3x + 1)(x-4)=0

3x + 1 = 0 ; x - 4 = 0

○Set each set of parenthesis equal to zero as separate equations.

▪Solve each "zeroed" equation independently

3x + 1 = 0 ; x - 4 = 0

3x + 1 = 0 ; x - 4 =0

3x = -1 ; x = 4

X = -1/3

▪Substitute the 2 values

○Check x = -1/3 in (3x + 1)(x – 4) = 0: 

 (3-1/3 + 1)(-1/3 – 4) = 0

(-1 + 1)(-4 1/3) 0

0=0

○

Check x = 4 in (3x + 1)(x - 4) = 0: 

(34 + 1)(4 – 4) = 0

(13)(0) = 0

0=0

◆ So, both solutions do "check" separately, and both are verified as working and correct for two different solutions.

Using the Quadratic Formula:

(The formula was attached to my answer to your question all you need to do is substiture the values of a, b, and c to the formula.)

Ex: For the equation 3x2 -5x - 8 = 0

a= 3

b= -5

c= -8