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
kirza4 [7]
2 years ago
5

X^+17x+72=12 factoring quadratic equation

Mathematics
1 answer:
Tom [10]2 years ago
8 0

Answer:

The first term is, x2 its coefficient is 1 .

The middle term is, -17x its coefficient is -17 .

The last term, "the constant", is +60

Step-1 : Multiply the coefficient of the first term by the constant 1 • 60 = 60

Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -17 .

-60 + -1 = -61

-30 + -2 = -32

-20 + -3 = -23

-15 + -4 = -19

-12 + -5 = -17 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -5

x2 - 12x - 5x - 60

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

x • (x-12)

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

5 • (x-12)

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

(x-5) • (x-12)

Which is the desired factorization

Equation at the end of step

1

:

(x - 5) • (x - 12) = 0

STEP

2

:

Theory - Roots of a product

2.1 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.

Solving a Single Variable Equation:

2.2 Solve : x-5 = 0

Add 5 to both sides of the equation :

x = 5

Solving a Single Variable Equation:

2.3 Solve : x-12 = 0

Add 12 to both sides of the equation :

x = 12

Supplement : Solving Quadratic Equation Directly

Solving x2-17x+60 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-17x+60

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 8.5000

Plugging into the parabola formula 8.5000 for x we can calculate the y -coordinate :

y = 1.0 * 8.50 * 8.50 - 17.0 * 8.50 + 60.0

or y = -12.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-17x+60

Axis of Symmetry (dashed) {x}={ 8.50}

Vertex at {x,y} = { 8.50,-12.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 5.00, 0.00}

Root 2 at {x,y} = {12.00, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2-17x+60 = 0 by Completing The Square .

Subtract 60 from both side of the equation :

x2-17x = -60

Now the clever bit: Take the coefficient of x , which is 17 , divide by two, giving 17/2 , and finally square it giving 289/4

Add 289/4 to both sides of the equation :

On the right hand side we have :

-60 + 289/4 or, (-60/1)+(289/4)

The common denominator of the two fractions is 4 Adding (-240/4)+(289/4) gives 49/4

So adding to both sides we finally get :

x2-17x+(289/4) = 49/4

Adding 289/4 has completed the left hand side into a perfect square :

x2-17x+(289/4) =

(x-(17/2)) • (x-(17/2)) =

(x-(17/2))2

Things which are equal to the same thing are also equal to one another. Since

x2-17x+(289/4) = 49/4 and

x2-17x+(289/4) = (x-(17/2))2

then, according to the law of transitivity,

(x-(17/2))2 = 49/4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x-(17/2))2 is

(x-(17/2))2/2 =

(x-(17/2))1 =

x-(17/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x-(17/2) = √ 49/4

Add 17/2 to both sides to obtain:

x = 17/2 + √ 49/4

Since a square root has two values, one positive and the other negative

x2 - 17x + 60 = 0

has two solutions:

x = 17/2 + √ 49/4

or

x = 17/2 - √ 49/4

Note that √ 49/4 can be written as

√ 49 / √ 4 which is 7 / 2

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2-17x+60 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = -17

C = 60

Accordingly, B2 - 4AC =

289 - 240 =

49

Applying the quadratic formula :

17 ± √ 49

x = —————

2

Can √ 49 be simplified ?

Yes! The prime factorization of 49 is

7•7

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 49 = √ 7•7 =

± 7 • √ 1 =

± 7

So now we are looking at:

x = ( 17 ± 7) / 2

Two real solutions:

x =(17+√49)/2=(17+7)/2= 12.000

or:

x =(17-√49)/2=(17-7)/2= 5.000

Two solutions were found :

x = 12

x = 5

Step-by-step explanation:

please mark my answer in brainlist

You might be interested in
A number from 1 to 100, inclusive, is selected at random. What is the probability that the
Gala2k [10]

Answer:i might be wrong but i believe its b

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Consider the graph of the linear function h(x) = –6 + x. Which quadrant will the graph not go through and why?
Lesechka [4]
H ( x ) = - 6 + x
m = 1 ( the slope )
b = - 6 ( y - intercept )
x - intercept: 
0 = - 6 + x
x = 6 
The graph is going through Quadrants:  I, II and IV.
Answer:
B ) Quadrant II, because the slope is positive and y-intercept is negative.
6 0
3 years ago
Read 2 more answers
The length of a rectangle is represented by the function L(x) = 5x. The width of that same rectangle is represented by the funct
Mazyrski [523]

Remember that the area of a rectangle is the length of the rectangle multiplied by the width of the rectangle.


In this case, we could say (where A(x) is the area of the rectangle):

A(x) = L(x) \cdot W(x)


Substituting the values the problem gave us for L(x) and W(x), we can find the formula for A in terms of x, which is:

A(x) = (5x) \cdot (2x^2 - 4x + 13) = (10x^3 - 20x^2 + 65x)


The formula for the area of the rectangle would be A(x) = 10x³ - 20x² + 65x.

3 0
3 years ago
Read 2 more answers
3m = 14.4
lubasha [3.4K]

Answer: 4 hours

Step-by-step explanation:

okay so you have to know your times tables 2*4=8 so 20*40=80 then if he paid a tip of 10$ that would equal $90 witch is what he paid.

4 0
2 years ago
A line has a y-intercept at (0,4) and an x-intercept at (6,0). What is the slope of the line?
Iteru [2.4K]
3/2 is the answer
i say this because you have to think of the problem as

4y=6x

divide the 4

y=6x/4

simplify
3/2
7 0
3 years ago
Read 2 more answers
Other questions:
  • The interior angles formed by the sides of a quadrilateral have measures that sum to 360°.
    5·2 answers
  • If 9x is an odd integer, represent the next odd integer as the algebraic expression in x.
    8·1 answer
  • Is 1/5 a rational number?? I need help ASAP
    9·2 answers
  • What is 1928626218192727x81182928287228288237
    5·1 answer
  • Excess cash on hand may be a problem for a problem for a company because it may miss an opportunity to___.
    11·1 answer
  • Pls help me with these 3 problems. <br>* click the picture *​
    7·1 answer
  • What is the range of an exponential parent function with base 2?
    10·2 answers
  • Please help! Will mark Brainliest.<br> Combine and Simplify: 48 (1/4x - 1/3y - 2/6x - 3/8y - 2/3
    6·1 answer
  • If you translate Point A ( 1 , 3 ) using the rule ( X , Y ) --&gt; ( X + 2 , Y + 5 ) then A' coordinates
    15·1 answer
  • Triangle prism surface area
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!