Question

factorise
${x}^{2} + 25x + 100 = 0$

Answer 1

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------>>>>Here is your answer<<<<--------

${x}^{2} + 25x + 100 = 0$

>>${x}^{2} + 20x + 5x + 100 = 0$

>>$x(x + 20) + 5(x + 20) = 0$

>>$(x + 5)(x + 20)$

>>$x = - 5 \: and \: x = - 20$

HOPE IT HELPS YOU..

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Answer 2

Answer:

Factoring  x2-25x+100 

The first term is,  x2  its coefficient is  1 .

The middle term is,  -25x  its coefficient is  -25 .

The last term, "the constant", is  +100 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 100 = 100 

Step-2 : Find two factors of  100  whose sum equals the coefficient of the middle term, which is   -25 .

     -100   +   -1   =   -101     -50   +   -2   =   -52     -25   +   -4   =   -29     -20   +   -5   =   -25   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  -5 

                     x2 - 20x - 5x - 100

Step-4 : Add up the first 2 terms, pulling out like factors :

                    x • (x-20)

              Add up the last 2 terms, pulling out common factors :

                    5 • (x-20)

Step-5 : Add up the four terms of step 4 :

                    (x-5)  •  (x-20)

             Which is the desired factorization

Equation at the end of step1:

(x - 5) • (x - 20) = 0

STEP2:Theory - Roots of a product

 2.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

 2.2      Solve  :    x-5 = 0 

 Add  5  to both sides of the equation : 

                      x = 5

Solving a Single Variable Equation:

 2.3      Solve  :    x-20 = 0 

 Add  20  to both sides of the equation : 

                      x = 20

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