SOLUTION: (x^2+7x)/2 =-3 I need help with this . Can someone please explain what to do for me using this example. I need to know the steps as well as how you got the answer. Thankyou for

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: (x^2+7x)/2 =-3 I need help with this . Can someone please explain what to do for me using this example. I need to know the steps as well as how you got the answer. Thankyou for       Log On


   

Question 213437: (x^2+7x)/2 =-3
I need help with this . Can someone please explain what to do for me using this example. I need to know the steps as well as how you got the answer. Thankyou for you time. Your are appreshated.

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
(x^2+7x)/2 =-3

The following steps solve the above equation

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=-1,x=-6.
  • Graphical form: Equation %28x%5E2%2B7x%29%2F2=-3 was fully solved.
  • Text form: (x^2+7x)/2=-3 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%28x%5E2%2B7x%29%2F2=-3+%29
    For tutors: simplify_cartoon( (x^2+7x)/2=-3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %28x%5E2%2B7%2Ax%29%2F2=highlight_red%28+-3+%29.
Moved these terms to the left highlight_green%28+3+%29
It becomes %28x%5E2%2B7%2Ax%29%2F2%2Bhighlight_green%28+3+%29=0.
Look at highlight_red%28+%28x%5E2%2B7%2Ax%29%2F2+%29%2B3=0.
Expanded term 1%2F2 by using associative property on %28x%5E2%2B7%2Ax%29
It becomes highlight_green%28+1%2F2%2Ax%5E2+%29%2Bhighlight_green%28+1%2F2%2A7%2Ax+%29%2B3=0.
Look at highlight_red%28+1+%29%2F2%2Ax%5E2%2B1%2F2%2A7%2Ax%2B3=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes x%5E2%2F2%2B1%2F2%2A7%2Ax%2B3=0.
Look at x%5E2%2F2%2Bhighlight_red%28+1+%29%2F2%2Ahighlight_red%28+7+%29%2Ax%2B3=0.
Multiplied numerator integers
It becomes x%5E2%2F2%2Bhighlight_green%28+7+%29%2F2%2Ax%2B3=0.
Look at highlight_red%28+x%5E2%2F2%2B7%2F2%2Ax%2B3+%29=0.
Equation highlight_red%28+x%5E2%2F2%2B7%2F2%2Ax%2B3=0+%29 is a quadratic equation: 0.5*x^2+3.5*x+3 =0, and has solutions -1,-6
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-1,x=-6.

Universal Simplifier and Solver


Done!



Based on the above quadratic equation

x%5E2%2F2%2B7x%2F2%2B3=0

you can use the quadratic formula

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

where a=1/2, b=7/2, and c=0

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 0.5x%5E2%2B3.5x%2B3+=+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=%283.5%29%5E2-4%2A0.5%2A3=6.25.

Discriminant d=6.25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3.5%2B-sqrt%28+6.25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283.5%29%2Bsqrt%28+6.25+%29%29%2F2%5C0.5+=+-1
x%5B2%5D+=+%28-%283.5%29-sqrt%28+6.25+%29%29%2F2%5C0.5+=+-6

Quadratic expression 0.5x%5E2%2B3.5x%2B3 can be factored:
0.5x%5E2%2B3.5x%2B3+=+0.5%28x--1%29%2A%28x--6%29
Again, the answer is: -1, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.5%2Ax%5E2%2B3.5%2Ax%2B3+%29



Also, note the parabola intercepts the x-axis at x=-1 and x=-6 (solutions to quadratic equation)

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J



I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J