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
DIA [1.3K]
2 years ago
6

Solve by completing the square and hunt for twice the larger root. x^2-9x+3=0

Mathematics
2 answers:
Agata [3.3K]2 years ago
4 0

Step-by-step explanation:

Simplifying

x2 + -9x + -3 = 0

Reorder the terms:

-3 + -9x + x2 = 0

Solving

-3 + -9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.

-3 + -9x + 3 + x2 = 0 + 3

Reorder the terms:

-3 + 3 + -9x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0

0 + -9x + x2 = 0 + 3

-9x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3

-9x + x2 = 3

The x term is -9x.  Take half its coefficient (-4.5).

Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.

-9x + 20.25 + x2 = 3 + 20.25

Reorder the terms:

20.25 + -9x + x2 = 3 + 20.25

Combine like terms: 3 + 20.25 = 23.25

20.25 + -9x + x2 = 23.25

Factor a perfect square on the left side:

(x + -4.5)(x + -4.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting

(x + -4.5) equal to 4.82182538 and -4.82182538.

Subproblem 1

x + -4.5 = 4.82182538

Simplifying

x + -4.5 = 4.82182538

Reorder the terms:

-4.5 + x = 4.82182538

Solving

-4.5 + x = 4.82182538

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.5' to each side of the equation.

-4.5 + 4.5 + x = 4.82182538 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0

0.0 + x = 4.82182538 + 4.5

x = 4.82182538 + 4.5

Combine like terms: 4.82182538 + 4.5 = 9.32182538

x = 9.32182538

Simplifying

x = 9.32182538

Subproblem 2

x + -4.5 = -4.82182538

Simplifying

x + -4.5 = -4.82182538

Reorder the terms:

-4.5 + x = -4.82182538

Solving

-4.5 + x = -4.82182538

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.5' to each side of the equation.

-4.5 + 4.5 + x = -4.82182538 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0

0.0 + x = -4.82182538 + 4.5

x = -4.82182538 + 4.5

Combine like terms: -4.82182538 + 4.5 = -0.32182538

x = -0.32182538

Simplifying

x = -0.32182538

Solution

The solution to the problem is based on the solutions

from the subproblems.

x = {9.32182538, -0.32182538}

svetoff [14.1K]2 years ago
4 0

Answer:

I can anwser the fist part but im not sure what you mean by hunt for twice the larger root. But by completing the square your overall end result by rounding to the hundreths place would be x= (8.65, 0.35)

Step-by-step explanation:

You might be interested in
The expression c(16x + 14) is equivalent to 32x + d.
pychu [463]

Answer:

c = 2

d = 28

Step-by-step explanation:

Please see the attached file for explanation

7 0
2 years ago
What is the factorization of the trinomial below?
lidiya [134]

Answer:

B)

Step-by-step explanation:

4 0
2 years ago
A ferry boat travels 167 miles in one week. How many miles does the boat travel in 3 weeks?
Dafna11 [192]
The boat travels 501 miles in 3 weeks.
6 0
3 years ago
Read 2 more answers
Ty and his 3 brothers share a pizza equally. Which of these shows how much of the pizza Ty's brothers have?
Yuki888 [10]

Answer:

3/4

Step-by-step explanation:

pizza is cut into fourths because there are for people eating it. the brothers have 3/4 of the pizza because there are only 3 brothers

7 0
3 years ago
This is my last question I need to do what’s the answer
MAXImum [283]

Step-by-step explanation:

According to the question,

l+5=2h

5 0
3 years ago
Other questions:
  • Which of the following binomials is a factor of x cubed plus 4 x squared plus x minus 6?
    8·1 answer
  • The length of a pole is to be 6.5 ft.The actual length of the pole may vary by as much as 0.02ft. Write an absolute value inequa
    13·1 answer
  • Nolan surveyed 350 students at his middle school. Pizza was the favorite lunch of 42% of the students. How many students chose p
    10·1 answer
  • The volume of the oblique cylinder is 24 ft^3. Which statements are true? Check all that apply.
    11·2 answers
  • Thomas made 8700mL of tomato soup. He packed 1.6L of the soup in his kids' lunches. He then froze half of the remaining soup. Ho
    12·1 answer
  • 12x + 3y = 15 for x = -1,0,1
    13·1 answer
  • Can someone help me with question 2
    15·1 answer
  • Please respond ASAP (Free response be specific and explain ! thanks )
    15·1 answer
  • Please answer the question CORRECTLY with a logical explanation. You will get brainliest guaranteed.
    9·1 answer
  • In trapezoid TRAP, the parallel bases are TP and RA
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!