SOLUTION: Hi, I need as much help as I could possibly get in understanding how to solve quadratic equations Section 11.3. I am required to show all of the steps in detail of how I got the an

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi, I need as much help as I could possibly get in understanding how to solve quadratic equations Section 11.3. I am required to show all of the steps in detail of how I got the an      Log On


   

Question 360729: Hi, I need as much help as I could possibly get in understanding how to solve quadratic equations Section 11.3. I am required to show all of the steps in detail of how I got the answer. Could someone please assist me with this problem:
Directions state:
Use the quadratic formula to solve equation.
1.)
x^2 + 15x+56=0

Found 2 solutions by jim_thompson5910, ewatrrr:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
For more help with the Quadratic Formula, check out this solver

Solved by pluggable solver: Quadratic Formula
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 x%5E2%2B15%2Ax%2B56=0 ( notice a=1, b=15, and c=56)





x+=+%28-15+%2B-+sqrt%28+%2815%29%5E2-4%2A1%2A56+%29%29%2F%282%2A1%29 Plug in a=1, b=15, and c=56




x+=+%28-15+%2B-+sqrt%28+225-4%2A1%2A56+%29%29%2F%282%2A1%29 Square 15 to get 225




x+=+%28-15+%2B-+sqrt%28+225%2B-224+%29%29%2F%282%2A1%29 Multiply -4%2A56%2A1 to get -224




x+=+%28-15+%2B-+sqrt%28+1+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-15+%2B-+1%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-15+%2B-+1%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-15+%2B+1%29%2F2 or x+=+%28-15+-+1%29%2F2


Lets look at the first part:


x=%28-15+%2B+1%29%2F2


x=-14%2F2 Add the terms in the numerator

x=-7 Divide


So one answer is

x=-7




Now lets look at the second part:


x=%28-15+-+1%29%2F2


x=-16%2F2 Subtract the terms in the numerator

x=-8 Divide


So another answer is

x=-8


So our solutions are:

x=-7 or x=-8

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

*Note: format of a line for using the quadratic equaton 

ax^2 + bx + c = 0

x^2 + 15x + 56=0 (given in the necessary format, no preliminary steps need to be taken)

a = 1 b = 15 and c = 56

Using the quadratic formula to solve the equation.

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

x+=+%28-15+%2B-+sqrt%28+15%5E2-4%2A1%2A56+%29%29%2F%282%29+

x+=+%28-15+%2B-+sqrt%28+225-224+%29%29%2F%282%29+

x+=+%28-15+%2B-+sqrt%28+1+%29%29%2F%282%29+

x+=+%28-15+%2B-+1%29%2F%282%29+

x = -16/2 = -8

x = -14/2 = -7