1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
8_murik_8 [283]
3 years ago
10

Solve by factoring

32 - 4x" alt="x^{2} = 32 - 4x" align="absmiddle" class="latex-formula">
​
Mathematics
2 answers:
WITCHER [35]3 years ago
5 0

Answer:

x = - 8, x = 4

Step-by-step explanation:

Given

x² = 32 - 4x ( subtract 32 - 4x from both sides )

x² + 4x - 32 = 0 ← in standard form

(x + 8)(x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 4 = 0 ⇒ x = 4

alekssr [168]3 years ago
3 0

Move all terms to one side of the equation, usually the left, using addition or subtraction.

Factor the equation completely.

Set each factor equal to zero, and solve.

List each solution from Step 3 as a solution to the original equation.

First Example

x2 + 3x = 8x - 6

Step 1

The first step is to move all terms to the left using addition and subtraction. First, we will subtract 8x from each side.

x2 + 3x - 8x = 8x - 8x - 6

x 2 - 5x = -6

Now, we will add 6 to each side.

x2 - 5x + 6 = -6 + 6

x 2 - 5x + 6 = 0

With all terms on the left side, we proceed to Step 2.

Step 2

We identify the left as a trinomial, and factor it accordingly:

(x - 2)(x - 3) = 0

We now have two factors, (x - 2) and (x - 3).

Step 3

We now set each factor equal to zero. The result is two subproblems:

x - 2 = 0

and

x - 3 = 0

Solving the first subproblem, x - 2 = 0, gives x = 2. Solving the second subproblem, x - 3 = 0, gives x = 3.

Step 4

The final step is to combine the two previous solutions, x = 2 and x = 3, into one solution for the original problem.

x2 + 3x = 8x - 6

x = 2, 3

Solve by Factoring: Why does it work?

Examine the equation below:

ab = 0

If you let a = 3, then logivally b must equal 0. Similarly, if you let b = 10, then a must equal 0.

Now try letting a be some other non-zero number. You should observe that as long as a does not equal 0, b must be equal to zero.

To state the observation more generally, "If ab = 0, then either a = 0 or b = 0." This is an important property of zero which we exploit when solving by factoring.

When the example was factored into (x - 2)(x - 3) = 0, this property was applied to determine that either (x - 2) must equal zero, or (x - 3) must equal zero. Therefore, we were able to create two equations and determine two solutions from this observation.

A Second Example

5x3 = 45x

Step 1

Move all terms to the left side of the equation. We do this by subtracting 45x from each side.

5x3 - 45x = 45x - 45x

5x 3 - 45x = 0.

Step 2

The next step is to factor the left side completely. We first note that the two terms on the left have a greatest common factor of 5x.

5x(x2 - 9) = 0

Now, (x2 - 9) can be factored as a difference between two squares.

5x(x + 3)(x - 3) = 0

We are left with three factors: 5x, (x + 3), and (x - 3). As explained in the "Why does it work?" section, at least one of the three factors must be equal to zero.

Step 3

Create three subproblems by setting each factor equal to zero.

1.   5x = 0

2.   x + 3 = 0

3.   x - 3 = 0

Solving the first equation gives x = 0. Solving the second equation gives x = -3. And solving the third equation gives x= 3.

Step 4

The final solution is formed from the solutions to the three subproblems.

x = -3, 0, 3

Third Example

3x4 - 288x2 - 1200 = 0

Steps 1 and 2

All three terms are already on the left side of the equation, so we may begin factoring. First, we factor out a greatest common factor of 3.

3(x4 - 96x2 - 400) = 0

Next, we factor a trinomial.

3(x2 + 4)(x2 - 100) = 0

Finally, we factor the binomial (x2 - 100) as a difference between two squares.

3(x2 + 4)(x + 10)(x - 10) = 0

Step 3

We proceed by setting each of the four factors equal to zero, resulting in four new equations.

1.   3 = 0

2.   x2 + 4 = 0

3.   x + 10 = 0

4.   x - 10 = 0

The first equation is invalid, and does not yield a solution. The second equation cannot be solved using basic methods. (x2 + 4 = 0 actually has two imaginary number solutions, but we will save Imaginary Numbers for another lesson!) Equation 3 has a solution of x = -10, and Equation 4 has a solution of x = 10.

Step 4

We now include all the solutions we found in a single solution to the original problem:

x = -10, 10

This may be abbreviated as

x = ±10

Hope this helps!!

You might be interested in
What is the classifications of polynomials -gh4i+3g5
Step2247 [10]

Answer:

The polynomial -gh⁴i + 3g⁵ is a binomial, since it has two terms

Degree of polynomial: degree of a polynomial is the term with highest of exponent.

Degree of binomial -gh⁴i + 3g⁵ = 6

1st term(-gh⁴i ) = (power of g = 1, power of h = 4, power of i = 1)

2nd term(3g⁵) = (power of g = 5)

the polynomial -gh⁴i + 3g⁵ is a 6 degree binomial.

5 0
3 years ago
Here is a rectangle.
NISA [10]

Step-by-step explanation:

Let the area of rectangle with given points are as follows :

A(-3,3)

B(3,2)

C(4,-1) = C( x1,y1)

D(-2,-3) = D( x2, y2)

Now,

  1. The distance of CD = root under

(x2-x)^2 +( y2 - y1)^2

= root under (-2-4)^2 + ( -3+1)^2

= root under (-6)^2 + (-2)^2

= root under 36 + 4

= root under 40

= 2root 10

Therefore; the unit number if CD is 2 root 10.

6 0
2 years ago
Glenn ate 2 apples a day for a week. In addition to the apples, he ate 3 pears during the week. write the expression that shows
Mama L [17]

Answer:

17 pieces of fruit in total

Step-by-step explanation:

2x7=14+3=17

7 0
2 years ago
- Do two points always, sometimes, or never determine a line? Explain
White raven [17]

Answer:

Always

Step-by-step explanation:

if two points lie in a plane, then the entire line containing those points lies in that plane

8 0
3 years ago
Help!! I will give pints and brainlest pls!!! <br><br> (No Decimals!)
son4ous [18]

Answer:

2: 0.65

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Bill can type 19 words per minute faster than bob. their combined typing speed is 97 words per minute. find bobs typing speed
    15·2 answers
  • Can someone help me please.
    10·1 answer
  • Lauren, Rachel and Becca started a business over the summer. Their income was $500. The girls put in different amounts of work,
    13·1 answer
  • The value of w is:<br> show work for brainlist
    7·1 answer
  • Let f(x)=3x^2+6x find f(2)<br><br>A.-4<br>B. 0<br>C. 4<br>D. 8
    6·1 answer
  • Consider a left-tailed test, where the p-value is found to be 0.10. If the sample size n for this test is 49, then the t statist
    10·1 answer
  • Rose Marie is shopping for some new shoes. The shoes she wants cost
    14·1 answer
  • Hope has of an hour to play outside and do her homework. She wants to split her time equally between the twe activities much tim
    7·2 answers
  • I’m stuck on this question. I don’t know how to solve it.
    15·1 answer
  • Sketch a graph of x + y= -5
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!