Question

how to solve a^2 - 14a - 51 by mid-term splitting?

Answer 1

${a}^{2} - 14a - 51 \\ = {a}^{2} - 17a + 3a - 51 \\ = a(a - 17) + 3(a - 17) \\ = (a + 3)(a - 17)$

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Answer 2

Mid term splitting - also known as factorising

The formula to find the factors of an equation

Ax²-Bx+C =0 is:

[-b ± √(b²-4ac)] ÷ 2a

here :

• a - coefficient of X² term
• b - coefficient of X term
• c - constant term

in your case:

• a=1
• b=14
• c= -51

now substituting values in the above formula we get

the roots as A = -7±10

A = -7+10 ; A = -7-10

A=3 ;A = -17

Let me know if this helped !