SOLUTION: #1. 4t2−1t−4=0 Solve by the quadratic formula: #2. −6x2=−2x−20 Solve by the quadratic formula: #3. 3x2=−12x+15 Solve using the quadratic formula. List your a

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: #1. 4t2−1t−4=0 Solve by the quadratic formula: #2. −6x2=−2x−20 Solve by the quadratic formula: #3. 3x2=−12x+15 Solve using the quadratic formula. List your a      Log On


   

Question 1149179: #1. 4t2−1t−4=0
Solve by the quadratic formula:
#2. −6x2=−2x−20
Solve by the quadratic formula:
#3. 3x2=−12x+15
Solve using the quadratic formula. List your answers, separated by commas.
#4. 5x2−35=0
Solve using the quadratic formula. List your answers, separated by commas.
#5. 2x2−4=0

It must be in fraction form. It can not be done as a decimal.

Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4t^2 − t − 4 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-1x%2B-4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A4%2A-4=65.

Discriminant d=65 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+65+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+65+%29%29%2F2%5C4+=+1.13278221853732
x%5B2%5D+=+%28-%28-1%29-sqrt%28+65+%29%29%2F2%5C4+=+-0.882782218537319

Quadratic expression 4x%5E2%2B-1x%2B-4 can be factored:
4x%5E2%2B-1x%2B-4+=+%28x-1.13278221853732%29%2A%28x--0.882782218537319%29
Again, the answer is: 1.13278221853732, -0.882782218537319. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-1%2Ax%2B-4+%29

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Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

Solving quadratic equations is a  BASIC  ELEMENTARY  SKILL  each student  MUST  DEVELOPE  in his  (or her)  school years.

To help the students,  the lessons were created in this site
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
giving the general theory and examples.

Read them and learn on how to solve quadratic equations using the quadratic formula on your own,  once and for all.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Quadratic equations".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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Hey, in arithmetic, the first basic skill is to know that 2 x 2 = 4.
The second basic skill is to know the multiplication table.


In Algebra, the first basic skill is to know how to solve the simplest lihear equation ax + b = c.
The second basic skill is to know on how to solve a quadratic equation.


Therefore, when you come with questions, similar to that of your post, it is almost as if you come to ask "how many is 2 x 2".