Question

${a}^{2} - {21a}^{2} - 100 = 0$
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Answer 1

${a}^{2} - {21a}^{2} - 100 = 0$

$\implies \: 20 {a} = 100$

$\implies \: a = \huge \frac{100}{20}$

a= 5

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Answer 2

Answer:

Factoring a2-21a-100

The first term is, a2 its coefficient is 1 .

The middle term is, -21a its coefficient is -21 .

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 -21 .

-100 + 1 = -99

-50 + 2 = -48

-25 + 4 = -21 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -25 and 4

a2 - 25a + 4a - 100

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

a • (a-25)

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

4 • (a-25)

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

(a+4) • (a-25)

Which is the desired factorization

so answer is a=25