ong>Step-by-step explanation:

(1) x2" was REPLACED by "x^2".

Step by step solution :

STEP 1: Equation at the end of step 1

(2x2 + 24x) + 70 = 0

STEP 2: Pulling out like terms

STEP 3 : Pull out like factors :

3.1 2x2 + 24x + 70 = 2 • (x2 + 12x + 35)

Trying to factor by splitting the middle term

3.2 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

-5 + -7 = -12

-1 + -35 = -36

1 + 35 = 36

5 + 7 = 12 That's it

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

x2 + 5x + 7x + 35

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

x • (x+5)

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

7 • (x+5)

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

(x+7) • (x+5)

Which is the desired factorization

Equation at the end of step 3:

2 • (x + 7) • (x + 5) = 0

STEP 4 :

Theory - Roots of a product

4.1 A product of several terms equals zero.

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

We shall now solve each term = 0 SEPARATELY

In other words, we are GOING to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Equations which are never TRUE:

4.2 Solve : 2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.3 Solve : x+7 = 0

Subtract 7 from both sides of the equation :

x = -7

Solving a Single Variable Equation:

4.4 Solve : x+5 = 0

Subtract 5 from both sides of the equation :

x = -5

(m + 2) • (m - 7) = 0

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