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Indian Quadratic Math Problems










































x2 + 12x - 64 = 0

The Indian mathematical solution...

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Nov 07, 2011
Solve Quadratic Equation - Indian Method
by: Staff


Question:

x2 + 12x - 64 = 0

The Indian mathematical solution...



Answer:

x² + 12x - 64 = 0


The Indian Method for solving a quadratic equation is:

(a) Move the constant term to the right side of the equation.
(b) Multiply each term in the equation by four times the coefficient of the x squared term.
(c) Square the coefficient of the original x term and add it to both sides of the equation.
(d) Take the square root of both sides.
(e) Set the left side of the equation equal to the positive square root of the number on the right side and solve for x.
(f) Set the left side of equation equal to the negative square root of the number on the right side of the equation and solve for x.
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(a) Move the constant term to the right side of the equation.

x² + 12x - 64 = 0

x² + 12x - 64 + 64 = 0 + 64

x² + 12x + 0 = 0 + 64

x² + 12x = 0 + 64

x² + 12x = 64



(b) Multiply each term in the equation by four times the coefficient of the x squared term.

The coefficient of the x² term is 1.

x² + 12x = 64

(4 * 1) * (x² + 12x = 64)

(4) * (x² + 12x = 64)

(4)*x² + (4)*(12x) = (4)*(64)

4x² + 48x = 256



(c) Square the coefficient of the original x term and add it to both sides of the equation.

The coefficient of the original x term is 12.

(12)² = 144

4x² + 48x = 256

4x² + 48x + 144 = 256 + 144

4x² + 48x + 144 = 400



(d) Take the square root of both sides of the equation.

4x² + 48x + 144 = 400

Sqrt(4x² + 48x + 144) = Sqrt(400)

Sqrt(2x + 12)² = Sqrt(20²)

(2x + 12) = ±20


(divide each side of the equation by 2)

(2x + 12) / 2 = ±(20 / 2)

(x + 6) * (2 / 2) = ±(20 / 2)

(x + 6) * (1) = ±(20 / 2)

(x + 6) = ±(20 / 2)

(x + 6) = ±10


(subtract 6 from each side of the equation)

x + 6 - 6 = ±10 - 6

x + 0 = ±10 - 6

x = ±10 - 6



(e) Set the left side of the equation equal to the positive square root of the number on the right side.

x = +10 - 6

x = +4



(f) Set the left side of equation equal to the negative square root of the number on the right side of the equation and solve for x.

x = -10 – 6

x = -16



the final solution is: x = {-16, 4}


check the solution by substituting the two numerical values of x into the original equation

for x = -16

x² + 12x - 64 = 0

(-16)² + 12*(-16) - 64 = 0

256 - 192 - 64 = 0

256 - 256 = 0

0 = 0, OK


for x = 4

x² + 12x - 64 = 0

(4)² + 12*(4) - 64 = 0

16 + 48 - 64 = 0

64 - 64 = 0

0 = 0, OK







Thanks for writing.

Staff
www.solving-math-problems.com


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