Question

x2 - 3|x - 2| - 4x = - 6

Answer 1

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x^2-3*(x-2)-4*x-(-6)=0

Step by step solution :

STEP

1

:

Equation at the end of step 1

(((x2) - 3 • (x - 2)) - 4x) - -6 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring x2-7x+12

The first term is, x2 its coefficient is 1 .

The middle term is, -7x its coefficient is -7 .

The last term, "the constant", is +12

Step-1 : Multiply the coefficient of the first term by the constant 1 • 12 = 12

Step-2 : Find two factors of 12 whose sum equals the coefficient of the middle term, which is -7 .

-12 + -1 = -13

-6 + -2 = -8

-4 + -3 = -7 That's it

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

x2 - 4x - 3x - 12

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

x • (x-4)

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

3 • (x-4)

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

(x-3) • (x-4)

Which is the desired factorization

Equation at the end of step