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Using the Indian method, solve a. x^2 - 2x - 3 0, b. 4x^2

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Using the Indian method, solve a. x^2 - 2x - 3 = 0, b. 4x^2 - 4x - 3 = 0,
c. x^2 + 12x - 64 = 0, d. 2x^2 - 3x - 5 = 0?

abozer :

Hi,

abozer :

Let me give more detailed explanation for the first equation and then I will solve the others with less detail.

abozer :

a.

abozer :

x^2 - 2x - 3 = 0

abozer :

Take the constant term to the right side of the equation,

abozer :

x^2 - 2x = 3

abozer :

Multiply each term in the equation by four times the coefficient of the x^2 term,

abozer :

4x^2 - 8x = 12

abozer :

square the coefficient of the original x term and add it to both sides of the equation,

abozer :

4x^2 - 8x + 4 = 12 + 4

abozer :

4x^2 - 8x + 4 = 16

abozer :

left side of the equation is a perfect square,

abozer :

(2x - 2)^2 = 16

abozer :

take the squareroot of both sides,

Customer :

Hello,

abozer :

2x - 2 = -4 or 2x - 2 = 4

abozer :

2x = -2 or 2x = 6

abozer :

x = -1 or x = 3

abozer :

So the solution for the first part of your question is,

abozer :

x = -1, 3

abozer :

Part b.

abozer :

4x^2 - 4x - 3 = 0

abozer :

4x^2 - 4x = 3

Customer :

this is great, I was getting hung up on the 4 step subtracting the 4 instead of adding.

abozer :

64x^2 - 64x = 48

abozer :

64x^2 - 64x + 16 = 48 + 16

abozer :

(8x - 4)^2 = 64

abozer :

8x - 4 = -8 or 8x - 4 = 8

abozer :

8x = -4 or 8x = 12

abozer :

x = -4/8 or x = 12/8

abozer :

x = -1/2 or x = 3/2

abozer :

Part c.

abozer :

x^2 + 12x - 64 = 0

abozer :

x^2 + 12x = 64

abozer :

4x^2 + 48x = 256

abozer :

4x^2 + 48x + 144 = 256 + 144

abozer :

(2x + 12)^2 = 400

abozer :

2x + 12 = -20 or 2x + 12 = 20

abozer :

2x = -32 or 2x = 8

abozer :

x = -16 or x = 4

abozer :

Part d.

abozer :

2x^2 - 3x - 5 = 0

abozer :

2x^2 - 3x = 5

abozer :

16x^2 - 24x = 40

abozer :

16x^2 - 24x + 9 = 40 + 9

abozer :

(4x - 3)^2 = 49

abozer :

4x - 3 = -7 or 4x - 3 = 7

abozer :

4x = -4 or 4x = 10

abozer :

x = -4/4 or x = 10/4

abozer :

x = -1 or x = 5/2

abozer :

Let me know if you have any questions.

Customer :

Thank you for going through this, the errors I had were simple, but make a big difference. I'm learning through the comparison.

abozer :

That's very good.

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