![cork6](/avatars/49350.jpg)
cork6
01.11.2019 •
Mathematics
Solve by factoring
![x^{2} = 32 - 4x](/tex.php?f=x^{2} = 32 - 4x)
Solved
Show answers
More tips
- S Style and Beauty Intimate Haircut: The Reasons, Popularity, and Risks...
- A Art and Culture When Will Eurovision 2011 Take Place?...
- S Style and Beauty How to Choose the Perfect Hair Straightener?...
- F Family and Home Why Having Pets at Home is Good for Your Health...
- H Health and Medicine How to perform artificial respiration?...
- H Health and Medicine 10 Tips for Avoiding Vitamin Deficiency...
- F Food and Cooking How to Properly Cook Buckwheat?...
- F Food and Cooking How Many Grams Are In a Tablespoon?...
- L Leisure and Entertainment Carving: History and Techniques for Creating Vegetable and Fruit Decorations...
- P Photography and Videography How to Choose the Perfect Photo Paper for Your Images?...
Answers on questions: Mathematics
- M Mathematics The diameter of a speck of dust is about 0.00002 inches. Which of these is an appropriate estimate for the diameter of the speck of dust? 2×10−5in. 2×10−4in. 2×104in....
- M Mathematics Can someone Please help...
- M Mathematics Claire bought 180 candies and 140 pens for goody bags for her birthday. What is the largest number of goody bags that Claire can so that each goody bag has the...
- M Mathematics Please Help Asap thank you soo much god bless you...
- M Mathematics 1 of 1 Directions: Use the pictures in the box to answ Thanksgiving Meal Bread $6.95 Mashed Potatoes $4.70 Corn $3.20 the most expensive item? the least expensive...
- M Mathematics Fill in the table using this function rule. y = 4+4x X Y 2 3 4 10 Fill in the y area...
- M Mathematics Gina s mother bought 200 lollipops and 150 pencils for goody bags for Gina s birthday. What is the largest number of goody bags that Gina can make to get the same...
- M Mathematics June, Gavyn and Alex share some sweets in the ratio 2:2:1. June gets 14 sweets. How many did Alex get? brainlest for best answer...
- M Mathematics What is the value of this expression below when z=3 10z^2-2z-2...
- M Mathematics please help if you know! lesson name: L 10.5: Using the Distributive Property here is the pic i don t understand...
Ответ:
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!!
Ответ:
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
Ответ:
Step-by-step explanation:
The base units of length and volume are linked in the metric system. By definition, a liter is equal to the volume of a cube exactly 10 cm tall, 10 cm long, and 10 cm wide. Because the volume of this cube is 1000 cubic centimeters and a liter contains 1000 milliliters, 1 milliliter is equivalent to 1 cubic centimeter.