Decide equation using only factors to solve this problem 12x^{2} + 5x - 2 = 0

Emeli Hagan 2021-03-09 Answered
Decide equation using only factors to solve this problem
12x2 + 5x  2=0
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Answered 2021-03-10 Author has 109 answers

In order to factor the quadratic, we need to find the values of a, b and c for the given quadratic 12x2 + 5x  2=0 on comparing with standard quadratic
ax2 + bx + c=0
12x2 + 5x  2=0
a=12b=5, c= 2.
Now, let us apply ac method to factor the quadratic.
We got ac= 24 and b=5. So, we need to find the factors of -24, those add upto 5.
ac=12 2= 24(Product)
-24 could be factored in two numbers 8 and -3 that add upto 5.
Therefore, middle term 5x of expression 12x2 + 5x  2=0, could be break into two terms 8x and -3x.
Then we need to make the break the expression into groups.
Factor out 3x form 12x2  3x and factor out 2 from:
8x  2.
Then factor out common parenthesis (4x  1).
We got factored form (4x  1)(3x + 2)=0
12x2 + 5x  2=0
(12x2  3x) + (8x  2)=0
3x(4x  1) + 2(4x  1)=0
Factor out common parenthesis (4x  1)
(4x  1)(3x + 2)=0
By applying zero product rule, we need to set each factor equal to zero and solve for x.
We got x=14, 23.
4x  1=0 or 3x + 2=0
4x4=14 or 3x3=23
x=1.4 or x=23

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-03-02
In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a conference
asked 2020-11-01
Solve the following problems applying Polya’s Four-Step Problem-Solving strategy.
If six people greet each other at a meeting by shaking hands with one another, how many handshakes take place?
asked 2021-02-25
Means =59.47444,SDS=12.91711,Min=23.599,Max=82.603 AND Means =67.00742,SDS=12.7302,Min=39.613,Max=82.603 Means Based on your findings write a preliminary statistical report that comprises of the Methods, Results/Analysis and Conclusions sections. Include a comparison of the two distributions in (1) and (2) in terms of their central tendencies and variability. While your audience is one that lacks statistical expertise you are still expected to correctly interpret the data and statistical analyses, in a manner that is understandable to your audience. Be mindful to present an impartial report that distinguishes conclusive and inferential statements for the audience.
asked 2021-01-07

Consider the region below ​f(x)=(6 x),above the​ x-axis, and between
x=0 and x=6.
Let xi be the midpoint of the i th subinterval.
Approximate the area of the region using six rectangles. Use the midpoints of each subinterval for the heights of the rectangles. The area is approximately how many square units?

asked 2022-04-30
Provide a thorough response to the two following questions.
1. What is hypothesis testing? Provide all basic components, including error types, with explanations.
2.What is the difference between chi-square goodness of fit and chi-square test of independence? What do they have in common?
asked 2021-02-25
Give a full answer for the given question: The covalent backbone of DNA and RNA consists of: ?
asked 2021-08-10

A local firm manufactures LED products that have a lifespan that is approximately normally distributed with a std. dev. of 30 hours. If a sample of 30 LED products has an average lifespan of 780 hours, find a 96% confidence interval for the population mean of all LED products produced by this firm.
Choose 2 answers in nearest unit (ones) or in whole number.
Example, if your answer is 888.83μ899.56, choose 889 and 900.