SOLUTION: I'm lost. I've included the work I think is right. Solve the following quadratic equations. Make sure to show all your work. Use graphing to complete. 1. 3x2 + 11x – 20 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: I'm lost. I've included the work I think is right. Solve the following quadratic equations. Make sure to show all your work. Use graphing to complete. 1. 3x2 + 11x – 20 = 0       Log On


   

Question 98239: I'm lost. I've included the work I think is right.
Solve the following quadratic equations. Make sure to show all your work. Use graphing to complete.
1. 3x2 + 11x – 20 = 0
• Graphing Method
• 3x2+11x-20=0
• 3x2+11x-20+20=0+20
• 3x2+11x=20
• X2+11/3=20/3
•

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve 3%2Ax%5E2%2B11%2Ax-20=0 ( notice a=3, b=11, and c=-20)

x+=+%28-11+%2B-+sqrt%28+%2811%29%5E2-4%2A3%2A-20+%29%29%2F%282%2A3%29 Plug in a=3, b=11, and c=-20



x+=+%28-11+%2B-+sqrt%28+121-4%2A3%2A-20+%29%29%2F%282%2A3%29 Square 11 to get 121



x+=+%28-11+%2B-+sqrt%28+121%2B240+%29%29%2F%282%2A3%29 Multiply -4%2A-20%2A3 to get 240



x+=+%28-11+%2B-+sqrt%28+361+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-11+%2B-+19%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-11+%2B-+19%29%2F6 Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

x+=+%28-11+%2B+19%29%2F6 or x+=+%28-11+-+19%29%2F6

Lets look at the first part:

x=%28-11+%2B+19%29%2F6

x=8%2F6 Add the terms in the numerator
x=4%2F3 Divide

So one answer is
x=4%2F3



Now lets look at the second part:

x=%28-11+-+19%29%2F6

x=-30%2F6 Subtract the terms in the numerator
x=-5 Divide

So another answer is
x=-5

So our solutions are:
x=4%2F3 or x=-5

Notice when we graph 3%2Ax%5E2%2B11%2Ax-20, we get:

+graph%28+500%2C+500%2C+-15%2C+14%2C+-15%2C+14%2C3%2Ax%5E2%2B11%2Ax%2B-20%29+

and we can see that the roots are x=4%2F3 and x=-5. This verifies our answer