SOLUTION: (x^2⁄2)- 4 – 6x = - 4 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.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: (x^2⁄2)- 4 – 6x = - 4 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.       Log On


   

Question 213438: (x^2⁄2)- 4 – 6x = - 4
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.
Found 2 solutions by stanbon, drj:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(x^2⁄2)- 4 – 6x = - 4
---
Add 4 to both sides to get:
(x^2/2) - 6x = 0
---
Factor out the common factor of "x":
x[(x/2)-6] = 0
x = 0 or (x/2)-6 = 0
x = 0 or (x/2) = 6
x= 0 or x = 12
=====================
Cheers,
Stan H.

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2%29%2F2-4%966x=-4+

The following steps will simplify and solve the equation.

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


YOUR ANSWER


  • This is an equation! Solutions: x=12,x=0.
  • Graphical form: Equation %28x%5E2%29%2F2-4-6x=-4 was fully solved.
  • Text form: (x^2)/2-4-6x=-4 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%28x%5E2%29%2F2-4-6x=-4+%29
    For tutors: simplify_cartoon( (x^2)/2-4-6x=-4 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28highlight_red%28+x%5E2+%29%29%2F2+%29-4-6%2Ax=-4.
Remove unneeded parentheses around factor highlight_red%28+x%5E2+%29
It becomes highlight_green%28+x%5E2+%29%2F2-4-6%2Ax=-4.
Look at x%5E2%2F2-highlight_red%28+4+%29-6%2Ax=-4.
Moved -4 to the right of expression
It becomes x%5E2%2F2-6%2Ax-highlight_green%28+4+%29=-4.
Look at x%5E2%2F2-6%2Ax-4=highlight_red%28+-4+%29.
Moved these terms to the left highlight_green%28+4+%29
It becomes x%5E2%2F2-6%2Ax-4%2Bhighlight_green%28+4+%29=0.
Look at x%5E2%2F2-6%2Ax-highlight_red%28+4+%29%2Bhighlight_red%28+4+%29=0.
Added fractions or integers together
It becomes x%5E2%2F2-6%2Ax%2Bhighlight_green%28+0+%29=0.
Look at x%5E2%2F2-6%2Ax%2Bhighlight_red%28+0+%29=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes x%5E2%2F2-6%2Ax=0.
Look at highlight_red%28+x%5E2%2F2-6%2Ax+%29=0.
Equation highlight_red%28+x%5E2%2F2-6%2Ax=0+%29 is a quadratic equation: 0.5*x^2-6*x =0, and has solutions 12,0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=12,x=0.

Universal Simplifier and Solver


Done!



You can also use the quadratic formula given as

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

where a=1/2, b=-6, 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%2B-6x%2B0+=+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=%28-6%29%5E2-4%2A0.5%2A0=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+36+%29%29%2F2%5C0.5+=+12
x%5B2%5D+=+%28-%28-6%29-sqrt%28+36+%29%29%2F2%5C0.5+=+0

Quadratic expression 0.5x%5E2%2B-6x%2B0 can be factored:
0.5x%5E2%2B-6x%2B0+=+0.5%28x-12%29%2A%28x-0%29
Again, the answer is: 12, 0. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.5%2Ax%5E2%2B-6%2Ax%2B0+%29



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