SURENDRA K. answered • 07/17/14

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Nikky C.

asked • 07/17/141. Solve by completing square

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

3. Solve with quadratic formula

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SURENDRA K. answered • 07/17/14

An experienced,patient & hardworking tutor

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

Philip P. answered • 07/17/14

Affordable, Experienced, and Patient Algebra Tutor

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

SURENDRA K.

Hello Philip,

Yes, as per my methods,

I should have taken

2r-7= -9.899

r= -2.899

r= -1.4495

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07/17/14

Philip P.

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

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07/17/14

Nikky C.

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

Report

07/18/14

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Nikky C.

_{thanks so much the help is very appreciated!}07/18/14