Question

25 - (4x^2 - 12 +9)

Answer 1

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

4*x^2-12*x+9-(25)=0

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((22x2 - 12x) + 9) - 25 = 0
Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

4x2 - 12x - 16 = 4 • (x2 - 3x - 4)

Trying to factor by splitting the middle term

3.2 Factoring x2 - 3x - 4

The first term is, x2 its coefficient is 1 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -4

Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4

Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -3 .

-4 + 1 = -3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 1
x2 - 4x + 1x - 4

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 :
1 • (x-4)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-4)
Which is the desired factorization

Equation at the end of step 3 :

4 • (x + 1) • (x - 4) = 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.