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Math - Quadratic Equation











































solve equation in the Indian quadratic process x² - 2x - 13 = 0


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Jul 21, 2011
Solving a Quadratic Equation - Indian Method
by: Staff


The question:

solve equation in the Indian quadratic process x² - 2x - 13 = 0



The answer:


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 - 2x - 13 = 0

x² - 2x - 13 + 13 = 0 + 13

x² - 2x + 0 = 0 + 13

x² - 2x = 0 + 13

x² - 2x = 13


(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 - 2x = 13

(4 * 1) * (x² - 2x = 13)

(4) * (x² - 2x = 13)

(4)*x² + (4)*(- 2x) = (4)*(13)

4x² - 8x = 52


(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 -2.

(-2)² = 4

4x² - 8x = 52

4x² - 8x + 4 = 52 + 4

4x² - 8x + 4 = 56


(d) Take the square root of both sides.

4x² - 8x + 4 = 56

Sqrt(4x² - 8x + 4) = Sqrt(56)

Sqrt(2x - 2)² = Sqrt(2²*2*7)

Sqrt(2x - 2)² = Sqrt(2²)*Sqrt(14)

(2x - 2) = 2*Sqrt(14)

(to eliminate the 2’s on both sides of the equation, divide each side of the equation by 2)

(2x - 2)/2 = (2/2)*Sqrt(14)

(x - 1) = (1)*Sqrt(14)

x - 1 = (1)*Sqrt(14)


(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.

x - 1 = +Sqrt(14)

x - 1 + 1 = Sqrt(14) + 1

x + 0 = Sqrt(14) + 1

x = 1 + Sqrt(14)

x = 1 + 3.74166

x = 4.74166


(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 - 1 = -Sqrt(14)

x - 1 + 1 = -Sqrt(14) + 1

x + 0 = -Sqrt(14) + 1

x = 1 - Sqrt(14)

x = 1 - 3.74166

x = -2.74166


the final solution is: x = {-2.74166, 4.74166}


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

for x = -2.74166

x² - 2x - 13 = 0

(-2.74166)² - 2(-2.74166) - 13 = 0

7.51669 + 5.48332 - 13 = 0

13 - 13 = 0, OK


for x = 4.74166

x² - 2x - 13 = 0

(4.74166)² - 2(4.74166) - 13 = 0

22.4833 - 9.48332 - 13 = 0

13 - 13 = 0, OK



Thanks for writing.

Staff
www.solving-math-problems.com



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