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
mina [271]
1 year ago
11

Detmermine the best method to solve the following equation, then solve the equation. (3x-5)^2=-125

Mathematics
1 answer:
liq [111]1 year ago
3 0

For the given equation;

(3x-5)^2=-125

We shall begin by expanding the parenthesis on the left side, after which we would combine all terms on and move all of them to the left side, which shall yield a quadratic equation. Then we shall solve.

Let us begin by expanding the parenthesis;

\begin{gathered} (3x-5)^2\Rightarrow(3x-5)(3x-5) \\ (3x-5)(3x-5)=9x^2-15x-15x+25 \\ (3x-5)^2=9x^2-30x+25 \end{gathered}

Now that we have expanded the left side of the equation, we would have;

\begin{gathered} 9x^2-30x+25=-125 \\ \text{Add 125 to both sides and we'll have;} \\ 9x^2-30x+25+125=-125+125 \\ 9x^2-30x+150=0 \end{gathered}

We shall now solve the resulting quadratic equation using the quadratic formula as follows;

\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Where;} \\ a=9,b=-30,c=150 \\ x=\frac{-(-30)\pm\sqrt[]{(-30)^2-4(9)(150)}}{2(9)} \\ x=\frac{30\pm\sqrt[]{900-5400}}{18} \\ x=\frac{30\pm\sqrt[]{-4500}}{18} \\ x=\frac{30\pm\sqrt[]{-900\times5}}{18} \\ x=\frac{30\pm\sqrt[]{-900}\times\sqrt[]{5}}{18} \\ x=\frac{30\pm30i\sqrt[]{5}}{18} \\ \text{Therefore;} \\ x=\frac{30+30i\sqrt[]{5}}{18},x=\frac{30-30i\sqrt[]{5}}{18} \\ \text{Divide all through by 6, and we'll have;} \\ x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3} \end{gathered}

ANSWER:

x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3}

You might be interested in
Leah's house has media room with a large flat screen tv. The media room tv has a width of 8 feet and a height of 4.5 feet. The f
neonofarm [45]
The ratio of the media room tv's width to height is 8ft to 4.5ft or 8/4.5

since the ratio of the living room tv's width to height is the same, the ratio would be
x/27 = 8/4.5
with x being the living room tv's width. Solve for x
x = (8/4.5)(27)
   = 48
The width of the living room tv is 48 inches
4 0
3 years ago
Read 2 more answers
Help me out please i will give branliest and 25 points !!!
Margarita [4]

Answer:

Answers A (1/3), C (4/15) and D (5/6) are all repeating decimals.  

Step-by-step explanation:

Repeating decimals are decimals in which a number or sequence of numbers is repeated over and over when dividing the numerator by the denominator of a fraction.  For example, when you divide 1 by 3 (1/3), you will get a repeating decimal of 0.3333...since 3 goes into 10 three times with a remainder of 1 and will keep going.  Likewise, when you divide 4/15, you get an initial value of 0.2, with a repeating 6, or 0.266666...  Lastly, when you divide 5/6, you will get a repeating decimal of 0.833333....  The other answers will all be terminating decimals when you divide the numerator by the denominator.  Terminating decimals mean the stop at some point and don't continue.  

6 0
3 years ago
Read 2 more answers
Find the surface area of the composite solid.
Dvinal [7]

Answer:

281 ft^2

Step-by-step explanation:

We need to add each individual 2d shape together to find the surface area

Bottom: 5*12 = 60

Left side and right side: 4*5 = 20, 2 sides so 20*2= 40

Side facing us and side facing away from us: 12*4 = 48, 2 sides so 48*2=96

Top side that is cut by base of triangle: 7*5 = 35

Each triangle face: base = 5 (12-7), height = 5             1/2base * height so each triangle is .5*5*5 = 12.5; 4 triangles so 12.5*4=50

60+40+96+35+50=281

4 0
2 years ago
Read 2 more answers
15. • Solve the simultaneous equations
tamaranim1 [39]
Answer:
B. 1 and -2
Explanation:
First, add up the equations:
x-x+3y+y=4
4y=4
y=1
Now, plug y into any of the original equations above and solve for x:
-x+1=3
-x=2
x=-2
Therefore, the answer is B. 1 and -2
5 0
3 years ago
The cube of the difference of a number and 4.
Ugo [173]
It would be (N-4)^3.
5 0
3 years ago
Other questions:
  • How much has the value of y changed between the points (-8, 4) and (8, -4)?
    6·1 answer
  • A case of chocolate contains 15 chocolate bars. The chocolates come in three varieties milk, dark, and milk/dark mix. 6 milk cho
    6·1 answer
  • Can a equilateral triangle can be scalene
    15·2 answers
  • A manufacturing process produces integrated circuit chips. Over the long run the fraction of bad chips produced by the process i
    14·1 answer
  • Simplify if possible
    6·2 answers
  • Pls help
    10·1 answer
  • 80% of the students in Lea’s class earned an A or a B on the weekly math test. If 20 students got an A or a B, how many students
    11·2 answers
  • If ab=5 and a*a+b*b=25,then (a+b)(a+b)=?​
    6·1 answer
  • Hi! Please help I am very desperate and I need it solved. Thanks!
    6·1 answer
  • Caden removed the label of a soup can like the one shown. What is the approximate area of the label if the can is 4 inches high
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!