Question

Simplify the following:
X. 74+4 - (-2) +35 = 7​

Answer 1

Answer:

x^2+(12-x)^2-(74)=0

Step by step solution :

STEP

1

:

STEP

2

:

Pulling out like terms

2.1 Pull out like factors :

2x2 - 24x + 70 = 2 • (x2 - 12x + 35)

Trying to factor by splitting the middle term

2.2 Factoring x2 - 12x + 35

The first term is, x2 its coefficient is 1 .

The middle term is, -12x its coefficient is -12 .

The last term, "the constant", is +35

Step-1 : Multiply the coefficient of the first term by the constant 1 • 35 = 35

Step-2 : Find two factors of 35 whose sum equals the coefficient of the middle term, which is -12 .

-35 + -1 = -36

-7 + -5 = -12 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -5

x2 - 7x - 5x - 35

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

x • (x-7)

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

5 • (x-7)

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

(x-5) • (x-7)

Which is the desired factorization

Equation at the end of step

2

:

2 • (x - 5) • (x - 7) = 0

STEP

3

:

Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms