Question

solve: 6x²-35x +50=0​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

((2•3x2) - 35x) + 50

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 6x2-35x+50

The first term is, 6x2 its coefficient is 6 .

The middle term is, -35x its coefficient is -35 .

The last term, "the constant", is +50

Step-1 : Multiply the coefficient of the first term by the constant 6 • 50 = 300

Step-2 : Find two factors of 300 whose sum equals the coefficient of the middle term, which is -35 .

-300 + -1 = -301

-150 + -2 = -152

-100 + -3 = -103

-75 + -4 = -79

-60 + -5 = -65

-50 + -6 = -56

-30 + -10 = -40

-25 + -12 = -37

-20 + -15 = -35 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and -15

6x2 - 20x - 15x - 50

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

2x • (3x-10)

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

5 • (3x-10)

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

(2x-5) • (3x-10)

Which is the desired factorization

final result : (3x - 10) . ( 2x - 5)