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
vitfil [10]
3 years ago
9

Solve the radical equation.

Mathematics
2 answers:
Elena L [17]3 years ago
6 0

Answer:

There are no extraneous solutions

Step-by-step explanation:

sqrt(8x+9) = x+2

Square each side

(sqrt(8x+9))^2 = (x+2)^2

8x+9 =  (x+2)^2

FOIL

8x+9 = x^2 +2x+2x+4

Combine like term

8x+9 = x^2 +4x+4

Subtract 8x from each side

8x-8x+9 = x^2 +4x-8x+4

9 = x^2 -4x+4

Subtract 9 from each side

0 = x^2 -4x-5

Factor

0=(x-5) (x+1)

Using the zero product property\

x-5 =0  x+1=0

x=5   x=-1

Check the solutions

x=5

sqrt(8*5+9) = 5+2

sqrt(40+9) = 5+2

sqrt(49) =7

7=7

x=-1

sqrt(8*(-1)+9) = -1+2

sqrt(-8+9) = -1+2

sqrt(1) =1

1=1

Both solutions are true solutions

Scrat [10]3 years ago
4 0

Answer:

there are no extraneous solutions to the equation

Step-by-step explanation:

Given

\sqrt{8x+9} = x + 2 ( square both sides )

8x + 9 = (x + 2)² ← expand

8x + 9 = x² + 4x + 4 ( subtract 8x + 9 from both sides )

0 = x² - 4x - 5 ← in standard form

0 = (x - 5)(x + 1) ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 1 = 0 ⇒ x = - 1

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = 5 : \sqrt{8(5)+9} = \sqrt{49} = 7

right side = 5 + 2 = 7

left side = right side ⇒ x = 5 is a solution

x = - 1 : \sqrt{8(-1)+9} = \sqrt{1} = 1

right side = - 1 + 2 = 1

left side = right side ⇒ x = - 1 is a solution

There are no extraneous solutions

You might be interested in
HELP 20 POINTS!!! Does the infinite geometric series diverge or converge? Explain.
Nitella [24]

Answer:

c. it converges, it has a sum

8 0
3 years ago
Read 2 more answers
Is 0.18 a terminating, repeating, or non repeating decimal
Paha777 [63]

Answer:

a non repeating decimal

Step-by-step explanation:

answer from alexa device

6 0
3 years ago
Find L when P= 24 and W = 6.<br> P = 2L+ 2W (perimeter of a rectangle)<br> L =
Anon25 [30]

Answer:

6

Step-by-step explanation:

24 = 2L + 2(6), multiply...

24 = 2L + 12, subtract 12 to both sides...

12 = 2L, divide 2 to both sides to isolate the varibale L

6 = L

Therefroe, L = 6

8 0
2 years ago
Does someone mind helping me with this?
Contact [7]

Answer:

should be the 1st 2nd and the 4th one

Step-by-step explanation:

if not correct plz tell me

3 0
3 years ago
Y = -x^2 + 5<br> -x + y = 3<br> Solve algebraically pleaseee help!!!
SIZIF [17.4K]
2.37 I’m pretty sure
4 0
3 years ago
Other questions:
  • What is the base of a triangle with a height 2/3 in. and an area of 45in?
    5·1 answer
  • The chart shows the cost of 2 new vehicle. Which digit in the trucks price is one tenth of the value of that same digit in the c
    15·1 answer
  • BRAINLIEST ASAP! PLEASE ANSWER!!!!!
    6·1 answer
  • What is the surface area of the cylinder with height 7yds and radius 6yd? Round your answer to the nearest thousandth
    12·1 answer
  • What is the formula for a cylinder and a circle?
    13·1 answer
  • Which describes the slope of this line?
    10·2 answers
  • X + 2
    9·1 answer
  • Y−2x=4
    7·1 answer
  • NEED HELP ASAP GIVING 60 POINTS AND BRAINLIEST !!!What is the algebraic expression for the following word phrase: the quotient o
    13·1 answer
  • What is the LCF of 60 and 10 ?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!