SOLUTION: Solve by using the quadratic formula. (18/w^2) - (10/w) + 1 = 0 If your answer contains a radical, express it in simplified form. Do not convert to decimal form.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Solve by using the quadratic formula. (18/w^2) - (10/w) + 1 = 0 If your answer contains a radical, express it in simplified form. Do not convert to decimal form.      Log On


   

Question 213918: Solve by using the quadratic formula.
(18/w^2) - (10/w) + 1 = 0
If your answer contains a radical, express it in simplified form.
Do not convert to decimal form.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by using the quadratic formula.

%2818%2Fw%5E2%29+-+%2810%2Fw%29+%2B+1+=+0+

If your answer contains a radical, express it in simplified form.
Do not convert to decimal form.

Step 1. Multiply by w%5E2 to get rid of denominators

%28w%5E2%2A%2818%2Fw%5E2%29+-+%2810%2Fw%29+%2B+1%29+=+0

18+-+10w+%2B+w%5E2%29+=+0

OR

w%5E2-10w%2B18

Step 2. Using the quadratic formula

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

where a=1, b=-10 and c=18 yields the following steps

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-10x%2B18+=+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=%28-10%29%5E2-4%2A1%2A18=28.

Discriminant d=28 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+28+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+28+%29%29%2F2%5C1+=+7.64575131106459
x%5B2%5D+=+%28-%28-10%29-sqrt%28+28+%29%29%2F2%5C1+=+2.35424868893541

Quadratic expression 1x%5E2%2B-10x%2B18 can be factored:
1x%5E2%2B-10x%2B18+=+1%28x-7.64575131106459%29%2A%28x-2.35424868893541%29
Again, the answer is: 7.64575131106459, 2.35424868893541. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B18+%29



Step 4. Based on the above steps we can simplify the solutions as follows

x1=%2810%2Bsqrt%2828%29%29%2F2

x1=%285%2Bsqrt%287%2A4%29%29%2F2

x1=5%2B2sqrt%287%29%2F2

x1=5%2Bsqrt%287%29

AND

x2=%2810-sqrt%2828%29%29%2F2

x2=%285-sqrt%287%2A4%29%29%2F2

x2=5-2sqrt%287%2F2%29

x2=5-sqrt%287%29

Step 5. ANSWER: So solutions are x1=5%2Bsqrt%287%29 and x2=5-sqrt%287%29

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J