This post is about the **5 STEPS SOLUTIONS TO QUADRATIC EQUATIONS BY FACTORIZATION**. The process of solving quadratic equation using factorization method is a simple one. The following examples explain the processes the let to a valid root.

Consider the expression;

ax^{2} + bx + C = 0

where a ≠ 0

To solve quadratic equation, you need to find two numbers whose sum is equal to **b** and the product is equal to **ac. **This does not mean that the numbers must be **a** and **c. **By so doing, quadratic equation is best express as;

X^{2} + (sum of two numbers)X + (product of two numbers) = 0

The only sure way of getting these numbers is by practice. Here I will start with a simple one where

a = 1, b = 7 and c = 10 that is

x^{2} + 7x + 10 = 0

** Step1**

Finding two numbers whose sum is 7 and product is 10

Let see the numbers whose sum is 7

6 and 1

5 and 2

4 and 3

Note there are infinite pair of numbers whose sum is 7 but only a pair has their product equal to 10 and that is 2 and 5.

**Step2**

Expand the coefficient of x using the discovered numbers, that is 2 and 5

X^{2} + (2 + 5)x + 10 = 0

X^{2} + 2x + 5x + 10 = 0

**step3**

Putting bracket

(X^{2} + 2x) + ( 5x + 10 ) = 0

**Step4**

Factorizing

X(x + 2) + 5(x +2) = 0

Bring outside elements together

(x + 5)(x + 2)=0

**Step5**

Equate each bracket equal to 0

X + 5 = 0 and x + 2 = 0

X = -5 and x = -2

Note that the sign on numbers must change each time a number crosses over the equality sign. That is so easy.

Now try your hands on X^{2} – 7x + 6 = 0, answer is -1 and 6

Where a ≠ 1 and a ≠ 0

Consider 3X^{2} – 13x + 10 = 0

Remember that the sum of two numbers (the roots) must be equal to **b** and their product must be equal to **ac **provided

ax^{2} + bx + C = 0, a ≠ 0.

In 3X^{2} – 13x + 10 = 0, ac = 3×10 = 30

So therefore we need to find two numbers whose product is 30 and sum is -13. This is simple, it is valid that (-3)x(-10) = 30 and (-3) + (-10) = -13. Then the two numbers are -3 and -10

**Expanding**

3X^{2} – 3x – 10x + 10 = 0

**Bracketing**

(3X^{2} – 3x) – (10x + 10) = 0

**Factorizing**

3x(x – 1) -10(x – 1) = 0

**Bringing elements together**

(3x – 10)(x – 1) = 0

3x – 10 = 0 and x – 1 = 0

3x = 10 and x = 1

X = and x = 1

Now try your hands on 2X^{2} – 11x + 12 = 0

Answer 4 and

I hope this has help you on the** STEPS SOLUTIONS TO QUADRATIC EQUATIONS BY FACTORIZATION**.