1. Solve by completing square

2. Use the discriminant to find the number of unique real solutions

3. Solve with quadratic formula

1. Solve by completing square

2. Use the discriminant to find the number of unique real solutions

3. Solve with quadratic formula

Tutors, please sign in to answer this question.

San Diego, CA

4r^2 - 28r -49=0

4r^2 -28r + 49 -49 -49=0

4r^2 -28r + 49 = 98

(2r-7)^2 = 98

2r-7 = 9.899

2r = 16.899

r= 8.449

Olney, MD

Since Surendra answered the first question, I'll answer the next two. Let's put the equation into standard form:

4r^{2} - 28r - 49 = 0

2. The discriminant is b^{2} - 4ac where a=4, b= -28, and c= -49.

(-28)^{2} - (4)(4)(-49) = 784 + 784 = 1568

Since the discriminant is greater than zero, there will be two real solutions. (The rules are: discriminant<0, no real solutions; discriminant=0, one solution; discriminant>0, two solutions).

3. Solve using the quadratic formula:

r = (-b/2a) ± (1/2a)√(b^{2}-4ac)

Where a=4, b=-28, c=-49.

r = -(-28)/8 ± (1/8)√1568

r = 7/2 ± (7/2)√2

4{(7/2)(1+√2)}^{2} - 28{(7/2)(1+√2)} - 49 = 0

49 + 98√2 + 98 - 98 - 98√2 -49 = 0

49 - 49 = 0

CHECK!

4{(7/2)(1-√2)}^{2} - 28{(7/2)(1-√2)} - 49 = 0

49 - 98√2 + 98 - 98 + 98√2 - 49 = 0

49 - 98√2 + 98 - 98 + 98√2 - 49 = 0

49 - 49 = 0

CHECK !

1. Here's another take on problem 1 (complete the square):

4r^{2} - 28r = 49

4(r^{2} - 7r) = 49

r^{2} - 7r = 49/4

r^{2} - 7r + (-7/2)^{2} = 49/4 + (-7/2)^{2}

(r - (7/2))^{2} = 98/4

r - 7/2 = ±√(98/4) = ±(7/2)√2

4(r

r

r

(r - (7/2))

r - 7/2 = ±√(98/4) = ±(7/2)√2

Hello Philip,

Yes, as per my methods,

I should have taken

2r-7= -9.899

r= -2.899

r= -1.4495

Hi Surrendra,

No problem. I am the one who "liked" your answer since you posted a few minutes before I posted (not to mention that I made an error in my initial post). I subsequently revised my answer because I realized there is an exact solution without rounding decimals.

v/r, Phil

Thankyou for taking your time out to help me it means a lot!

Gilant P.

Miss Gil: Cares & Gets Results - Regents, SAT & NYS ELA & Math Exams

Jamaica, NY

4.8
(1404 ratings)

Nikunj P.

Math and Science Specialist, Over 14 Years of Educational Experience

Scarsdale, NY

4.9
(88 ratings)

Malik K.

MIT Grad, Math/Physics Tutor, Summer Math/Engineering Camp Instructor

New York, NY

5.0
(17 ratings)

- Algebra 2 2689
- Algebra 3770
- Math 6771
- Prealgebra 141
- Geometry 1372
- Algebra Help 868
- Algebra Word Problem 1910
- Math Help 3989
- Word Problem 3761
- Precalculus 1206

Find a tutor fast. Get the app.

Are you a tutor? Get the app for tutors

© 2005 - 2016 WyzAnt, Inc. - All Rights Reserved

## Comments

_{thanks so much the help is very appreciated!}