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**Date Submitted:** 09/17/2012 09:39 AM

Bernice Sapp

Week 3 Written Assignment

Math 126 Survey of Mathematical Methods

Instructor: Tonya Meisner

Date: 9/3/12

An interesting method for solving quadratic equations came from India. The steps are (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 square 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 the equation to the negative square root of the number on the right side of the equation and solve for X. Using this method I will solve the equations x^2-2-13=0 and 2x^2-3x-5=0. I will also select five numbers to substitute for x; 0 (zero), two even, and two odd for the equation: x^2- x+ 41. This is to see if it yields prime and composite numbers.

When solving the first equation (x^2 - 2x -13 = 0), we must add the additive inverse of a number to both sides of the equation to move it to the other side of it (x^2 - 2x -13 + 13 = 13 + 0) and use simple addition (x^2 - 2x = 13). Now to complete the square, take 1/2 of the 2 of coefficient ( -2x) to get -1 and square it to get 1 and add it to both side of the equation like so: x^2 - 2x + 1 = 1+ 13 - completing the square, x^2 - 2x + 1 = 14 - addition and (x-1)^ 2 = 14 - square rooting the x^2 -2x+1 or factoring. Taking the square root of both sides of the equation to remove the square out of the equation (sq rt. ((x-1) ^2) = sq rt. (14)). Square rooting both sides of the equation to remove the square and adding the (+ / -) because this equation as two answers (x -1 = +/- sq rt. (14)). Adding the additive inverse of a number to both sides of the equation to

move it to the other side of it (x-1 + 1 = 1 +/- sq rt. (14)). Therefore, x is equal to x = 1 +/- sq rt (14) when adding.

So with...