Question

Q- How i can solve quadratic equations with big numbers , faster . for example , 20x^2 - 157x + 222.?

Answer 1

Step 1 :

Equation at the end of step 1 :

((22•5x2) - 157x) + 222

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 20x2-157x+222

The first term is, 20x2 its coefficient is 20 .

The middle term is, -157x its coefficient is -157 .

The last term, "the constant", is +222

Step-1 : Multiply the coefficient of the first term by the constant 20 • 222 = 4440

Step-2 : Find two factors of 4440 whose sum equals the coefficient of the middle term, which is -157 .

-4440 + -1 = -4441

-2220+ -2 = -2222

-1480 + -3 = -1483

-1110 + -4 = -1114

-888 + -5 = -893

-740 + -6 = -746

-555 + -8 = -563

-444 + -10 = -454

-370 + -12 = -382

-296 + -15 = -311

-222 + -20 = -242

-185 + -24 = -209

-148 + -30 = -178

-120 + -37 = -157

That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -120 and -37

20x2 - 120x - 37x - 222

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

20x • (x-6)

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

37 • (x-6)

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

(20x-37) • (x-6)

Which is the desired factorization

Final result :

(x - 6) • (20x - 37)