2 answers

Solve using the quadratic formula

Question:

Solve using the quadratic formula.
5x^2-2x-3=0

Answers

Ok, remember that the quadratic formula is (-b+-sqrt(b^2 -4ac))/2a : so (2+-sqrt(4+60))/10. So that equals (2+-8)/10.  So you have two answers (2+8)/10 or (2-8)/10. 1 or -6/10.

.

{{{5x^2-3x-3=0}}} Start with the given equation. Notice that the quadratic {{{5x^2-3x-3}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=5}}}, {{{B=-3}}}, and {{{C=-3}}} Let's use the quadratic formula to solve for "x": {{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula {{{x = (-(-3) +- sqrt( (-3)^2-4(5)(-3) ))/(2(5))}}} Plug in {{{A=5}}}, {{{B=-3}}}, and {{{C=-3}}} {{{x = (3 +- sqrt( (-3)^2-4(5)(-3) ))/(2(5))}}} Negate {{{-3}}} to get {{{3}}}. {{{x = (3 +- sqrt( 9-4(5)(-3) ))/(2(5))}}} Square {{{-3}}} to get {{{9}}}. {{{x = (3 +- sqrt( 9--60 ))/(2(5))}}} Multiply {{{4(5)(-3)}}} to get {{{-60}}} {{{x = (3 +- sqrt( 9+60 ))/(2(5))}}} Rewrite {{{sqrt(9--60)}}} as {{{sqrt(9+60)}}} {{{x = (3 +- sqrt( 69 ))/(2(5))}}} Add {{{9}}} to {{{60}}} to get {{{69}}} {{{x = (3 +- sqrt( 69 ))/(10)}}} Multiply {{{2}}} and {{{5}}} to get {{{10}}}. {{{x = (3+sqrt(69))/(10)}}} or {{{x = (3-sqrt(69))/(10)}}} Break up the expression.

So the solutions are {{{x = (3+sqrt(69))/(10)}}} or {{{x = (3-sqrt(69))/(10)}}} which approximate to {{{x=1.131}}} or {{{x=-0.531}}}

.

Similar Solved Questions

1 answer
R1-12 R3- 22 R2 122 R4 -62 R5 32 R7 -62 Circle the nodes on the...
R1-12 R3- 22 R2 122 R4 -62 R5 32 R7 -62 Circle the nodes on the diagram, and label each node with a unique LETTER. Note: Terminals A and B are not considered nodes. 1. 2. How many nodes are in the circuit? How many branches are in the circuit? 3. 4. How many loops are in the circuit?...
1 answer
The Torrey Pine Corporation’s purchases from suppliers in a quarter are equal to 75 percent of...
The Torrey Pine Corporation’s purchases from suppliers in a quarter are equal to 75 percent of the next quarter’s forecast sales. The payables period is 60 days. Wages, taxes, and other expenses are 20 percent of sales, and interest and dividends are $90 per quarter. No capital expenditu...
1 answer
Please help with solving these problems they are measurement system conversion: 9.2 pounds (apothecary) = _____...
Please help with solving these problems they are measurement system conversion: 9.2 pounds (apothecary) = _____ drams 500 grains = ______ ounces 14 ounces = ______ grains 10 pints = ______ fluid drams 48 fluid ounces = _______ pints 20 fluid drams = ______ ml 231 drams = ______ pounds (apothecary) 6...
1 answer
3. Answer the following questions based on the reaction coordinate diagram below: Reaction pathway a. How...
3. Answer the following questions based on the reaction coordinate diagram below: Reaction pathway a. How many transition states are present? Label on the diagram. b. How many intermediates are present? Label on the diagram. c. Is the reaction endergonic or exergonic? d. What is the rate-limiting st...
1 answer
On January 1, 2017, Waterway Industries issued eight-year bonds with a face value of $6700000 and...
On January 1, 2017, Waterway Industries issued eight-year bonds with a face value of $6700000 and a stated interest rate of 6%, payable semiannually on June 30 and December 31. The bonds were sold to yield 8%. Table values are: On January 1, 2017, Waterway Industries issued eight-year bonds with a f...
1 answer
Eocell= -1.288V n = 3 When I calculate it K = 5.37*10^-66 but for some reason...
Eocell= -1.288V n = 3 When I calculate it K = 5.37*10^-66 but for some reason that answer is wrong. What am I doing wrong? Consider the following redox reaction, and answer the three questions below. 3 K+ (a q) + A1(s) rightarrow 3 K(s) + A13+(a q) Calculate E degree Number -1.288 v Calculate Delta ...
1 answer
What conclusion can be drawn from a comparison of the frog and rat data? [2 pt]...
What conclusion can be drawn from a comparison of the frog and rat data? [2 pt] the frog organ becomes proportionately smaller in larger individuals the rat organ becomes proportionately larger in smaller individuals What conclusion can be drawn from an analysis of the rat data? [2 p...
1 answer
Is the sequence geometric 2, 6, 18, 54,...?
Is the sequence geometric 2, 6, 18, 54,...?...
1 answer
Useveloped a small fecal impaction. 5. What teaching points and interventions are appropriate to prevent fecal...
useveloped a small fecal impaction. 5. What teaching points and interventions are appropriate to prevent fecal impaction? (USLO 1,6) Group Two: Ulcerative Colitis J.L, a 33-year old female, presents to the ED reporting the following: • 10 liquid, bloody stools in past 24 hours • Tenesmus (...
1 answer
On January 1, Renewable Energy issues bonds that have a $40,000 par value, mature in eight years, and pay 16% interest...
On January 1, Renewable Energy issues bonds that have a $40,000 par value, mature in eight years, and pay 16% interest semiannually on June 30 and December 31. 1. Prepare the journal entry for issuance assuming the bonds are issued at (a) 99 and (b) 10372. 2. How much interest does the company pay (...
1 answer
If sales are $820,000, variable costs are 55% of sales, and operating income is $260,000, what...
If sales are $820,000, variable costs are 55% of sales, and operating income is $260,000, what is the contribution margin ratio? a. 45% b. 55% c. 62% d. 32% ________2. A firm operated at 90% of capacity for the past year, during which fixed costs were $420,000, variab...
1 answer
A start-up biomedical engineering firm has begun manufacturing a drug-coated bimetallic stent, which is a thin...
A start-up biomedical engineering firm has begun manufacturing a drug-coated bimetallic stent, which is a thin wire mesh tube inserted in clogged coronary arteries to prop them open and prevent future heart attacks. Identify the following costs of manufacturing the stents as either sunk or avoidable...
1 answer
Question 2 (1 point) Draw the syndiotactic and isotactic structures for polyvinyl alcohol (structure shown below)...
Question 2 (1 point) Draw the syndiotactic and isotactic structures for polyvinyl alcohol (structure shown below) 7647 ууууу Syndiotactic Isotactic...
1 answer
How can structure securities create value?
How can structure securities create value?...
1 answer
Er ended The Alpine House, Inc., Is a large retailer of snow skis. The company assembled...
er ended The Alpine House, Inc., Is a large retailer of snow skis. The company assembled the information shown below for the quan March 31 Amount s150,eee s 758 Sales Selling price per pair of skis Variable selling expense per pair of skis Variable administrative expense per pair of skis Total fixed...
1 answer
Statistics HW problem
Andrew plans to retire in 40 years. He is thinking of investing his retirement funds in stocks, so he seeks out information on past returns. He learns that over the101 years from 1900 to 2000, the real (that is, adjusted for inflation) returns on U.S. common stocks had mean 8.7% and standard deviati...