SOLUTION: Solve by Factorization 1. x2 - 13x + 30 = 0 2. 2x2 - 3x = 2 3. 3x2 - 7x - 6 = 0 4. 5x2 - 40 x = 0 5. 36x2 - 81 = 0 6. 4x2 - 16 = 0 7. 3x2 = 4x + 7 8. x2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Solve by Factorization 1. x2 - 13x + 30 = 0 2. 2x2 - 3x = 2 3. 3x2 - 7x - 6 = 0 4. 5x2 - 40 x = 0 5. 36x2 - 81 = 0 6. 4x2 - 16 = 0 7. 3x2 = 4x + 7 8. x2      Log On


   

Question 188260: Solve by Factorization
1. x2 - 13x + 30 = 0
2. 2x2 - 3x = 2
3. 3x2 - 7x - 6 = 0
4. 5x2 - 40 x = 0
5. 36x2 - 81 = 0
6. 4x2 - 16 = 0
7. 3x2 = 4x + 7
8. x2 + 2x = 0
9. 5x2 - 40 x = 0
10. x2 + x = 0
Solve By Quadratic Formula
1. 2x2 - 6x + 3 = 0
2. 7x2 + 4x = 1
3. 2x2 + 6x + 3 = 0
4. x2 - 5x + 6 = 0
5. 3x2 = 4x + 5
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by Factorization
1. x2 - 13x + 30 = 0
This one is easy, you do it.
2. 2x2 - 3x = 2
2x^2 - 3x - 2 = 0
(2x + 1)*(x - 2) - 0
x = 2, x = -1/2
-------------------
3. 3x2 - 7x - 6 = 0
4. 5x2 - 40 x = 0
5. 36x2 - 81 = 0 Divide by 9
x^2 - 9 = 0
A difference of 2 squares is ALWAYS the product of the sum and difference of the roots.
sum = x + 3
difference = x - 3
(x+3)*(x-3)= 0
x = +3, x = -3
-----------------
6. 4x2 - 16 = 0 Divide by 4
7. 3x2 = 4x + 7
8. x2 + 2x = 0
9. 5x2 - 40 x = 0
10. x2 + x = 0
Solve By Quadratic Formula
1. 2x2 - 6x + 3 = 0
2. 7x2 + 4x = 1
3. 2x2 + 6x + 3 = 0
4. x2 - 5x + 6 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%2B6+=+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=%28-5%29%5E2-4%2A1%2A6=1.

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

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%28-5%29-sqrt%28+1+%29%29%2F2%5C1+=+2

Quadratic expression 1x%5E2%2B-5x%2B6 can be factored:
1x%5E2%2B-5x%2B6+=+%28x-3%29%2A%28x-2%29
Again, the answer is: 3, 2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B6+%29


5. 3x2 = 4x + 5
You can email me via the thank you note for assistance, or to check your work.