SOLUTION: Can anyone explain this to me, I am stumped and can't figure it out. Please I need help.. 1. 4X2 - 4X+3= 0 2. X2+12X-64=0 a. move the constant term to the right side of

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can anyone explain this to me, I am stumped and can't figure it out. Please I need help.. 1. 4X2 - 4X+3= 0 2. X2+12X-64=0 a. move the constant term to the right side of      Log On


   

Question 225322: Can anyone explain this to me, I am stumped and can't figure it out. Please I need help..


1. 4X2 - 4X+3= 0
2. X2+12X-64=0
a. move the constant term to the right side of the equation
b. multiply each term in the equation by four times the cofficient of the x2 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 slove for x
f. set the left side of the equation equal to the negative square root of the number on the right side of the equation and slove for x
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First let me say that this is an odd (and incomplete) way of completing the square. Anyway, let's proceed...

4x%5E2-4x+%2B+3+=+0
a. move the constant term to the right side of the equation
4x%5E2-4x+=+-3
b. multiply each term in the equation by four times the cofficient of the x2 term
4*4 = 16 so:
16%284x%5E2-4x%29+=+16%28-3%29
64x%5E2+-+64x+=+-48
c. square the coefficient of the original x term and add it to both sides of the equation
%28-4%29%5E2+=+16 so:
64x%5E2+-+64x+%2B+16+=+-32
A step that is missing here is to write the left side as a perfect square. After the steps so far the left side should fit one of the following patterns:
a%5E2+%2B2ab+%2B+b%5E2+=+%28a%2Bb%29%5E2 or a%5E2+-2ab+%2B+b%5E2+=+%28a-b%29%5E2. Your equation fits the second pattern with "8x" as "a" and "4" as "b":
%288x+-+4%29%5E2+=+-32
d. take the square root of both sides
At this point, with this equation, we have a problem. The left side is a perfect square. The right side is a negative number. Unless we are working with complex numbers, there are no perfect squares that are negative. So this equation has no solutions.

x%5E2+%2B+12x+-64+=+0
a. move the constant term to the right side of the equation
x%5E2+%2B+12x+=+64
b. multiply each term in the equation by four times the cofficient of the x2 term
4*1 = 4 so:
4%28x%5E2+%2B+12x%29+=+4%2864%29
4x%5E2+%2B+48x+=+256
c. square the coefficient of the original x term and add it to both sides of the equation
12%5E2+=+144 so:
4x%5E2+%2B+48x+%2B+144+=+400
Missing step: Rewrite as a perfect square. The left side fits the first perfect square pattern (see above) with "2x" as "a" and "12" as "b":
%282x+%2B+12%29%5E2+=+400
d. take the square root of both sides
sqrt%28%282x+%2B+12%29%5E2%29+=+sqrt%28400%29
e. set the left side of the equation equal to the positive square root of the number on the right side and slove for x
Since sqrt%28400%29+=+20:
2x + 12 = 20
2x = 8
x = 4
f. set the left side of the equation equal to the negative square root of the number on the right side of the equation and slove for x
2x + 12 = -20
2x = -32
x = -16