**Solving quadratic equations by factoring examples :**

Here we are going to see some example problems on solving quadratic equations using the method factoring.

Whenever we have a quadratic equation in the form ax² + bx + c and we need to factor this, first we have to check whether the coefficient of x² is 1 or not.

- If it is 1, then we have to take the constant term and split it into two factors.
- In which the product of two factors must be equal to the constant term and the simplified value of those factors equal to the middle term, that is coefficient of x.
- Write each factors is in the form (x + a) (x + b) according to the sign.
- Set each factors equal to zero to get the value of x.

- Multiply the coefficient of x² and constant term.
- Split this product into two factors such that their sum is equal to the coefficient of x .
- Divide each factors by the coefficient of x².
- If it is possible we can simplify, otherwise we have to write the denominator along with x.
- write each factors in the form (x + a) (x + b).
- Set each factors equal to zero to get the value of x.

**Example 1 :**

Solve x² + 9 x + 14 = 0

**Solution :**

**Since the coefficient of x**² is 1, split the constant term that into two parts.

14 = 2 ⋅ 7, 2 + 7 = 9

x² + 9 x + 14 = 0

(x + 2) (x + 7) = 0

x - 2 = 0 x + 7 = 0

x = 2, x = -7

Hence the solution is {2, -7}

Let us look into the next example problem on "Solving quadratic equations by factoring examples".

**Example**** 2 :**

Solve x² - 9 x + 14 = 0

**Solution :**

**Since the coefficient of x**² is 1, split the constant term that into two parts.

14 = -2 ⋅ (-7) , -2 - 7 = -9

x² - 9 x + 14 = (x - 2) (x - 7)

(x - 2) (x - 7) = 0

x - 2 = 0 x - 7 = 0

x = 2, x = 7

Hence the solution is {2, 7}

Let us look into the next example problem on "Solving quadratic equations by factoring examples".

**Example 3 :**

Solve x² + 2 x - 15 = 0

**Solution :**

**Since the coefficient of x**² is 1, split the constant term that into two parts.

-15 = -3 ⋅ 5 , -3 + 5 = 2

x² + 2 x - 15 = (x - 3) (x + 5)

(x - 3) (x + 5) = 0

x - 3 = 0 x + 5 = 0

x = 3, x = -5

Hence the solution is {3, -5}

**Example 4 :**

Solve x² - 2 x - 15 = 0

**Solution :**

**Since the coefficient of x**² is 1, split the constant term that into two parts.

-15 = -5 ⋅ 3 , -5 + 3 = -2

x² - 2 x - 15 = (x - 5) (x + 3)

(x - 5) (x + 3) = 0

x - 5 = 0 x + 3 = 0

x = 5, x = -3

Hence the solution is {-3, 5}

**Example 5 :**

Solve 2x² + 15 x + 27 = 0

**Solution :**

**Since the coefficient of x**² is not 1, multiply the coefficient of **x**² by the constant term and split it into two parts.

2 ⋅ 27 = 54

54 = 6 ⋅ 9 , 6 + 9 = 15

(x + 3) (2x + 9) = 0

x + 3 = 0 2x + 9 = 0

x = -3, x = -9/2

Hence the solution is {-3, -9/2}

**Example 6 :**

Solve 2x² - 15 x + 27 = 0

**Solution :**

**Since the coefficient of x**² is not 1, multiply the coefficient of **x**² by the constant term and split it into two parts.

2 ⋅ 27 = 54

54 = -6 ⋅ (-9) , -6 - 9 = -15

2x² - 6 x - 9x + 27 = 0

Factor 2x from the first two terms and factor 9 from the third and fourth terms

2x (x - 3) - 9(x - 3) = 0

(2x - 9) (x - 3) = 0

2x - 9 = 0, x - 3 = 0

2x = 9

x = 9/2 and x = 3

Hence the solution is {9/2, 3)

**Example 7 :**

Solve 2x² + 15 x - 27 = 0

**Solution :**

**Since the coefficient of x**² is not 1, multiply the coefficient of **x**² by the constant term and split it into two parts.

2 ⋅ (-27) = -54

-54 = 18 ⋅ (-3) , 18 - 3 = 15

2x² + 18 x - 3 x - 27 = 0

Factor 2x from the first two terms and factor 3 from the third and fourth terms

2x (x - 9) - 3(x - 9) = 0

(2x - 3) (x - 9) = 0

2x - 3 = 0, x - 9 = 0

2x = 9

x = 9/2 and x = 3

Hence the solution is {9/2, 3)

After having gone through the stuff given above, we hope that the students would have understood "Solving quadratic equations by factoring examples".

Apart from the stuff given above, if you want to know more about "Solving quadratic equations by factoring examples", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**