SOLUTION: Solve by completing the square. 4x^2 + 2x – 3 = 0 Hellllpppp, pleeeeeaaaaase!!!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve by completing the square. 4x^2 + 2x – 3 = 0 Hellllpppp, pleeeeeaaaaase!!!      Log On


   

Question 69254: Solve by completing the square.
4x^2 + 2x – 3 = 0
Hellllpppp, pleeeeeaaaaase!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2%2B2x-3=0Move the -3 to the right side by adding 3 to both sides
4%28x%5E2%2B%282%2F4%29x%29=3Factor out a 4 to get leading coefficient equal to 1
4%28x%5E2%2B%281%2F2%29%2Ax%2B__%29=3Complete the square by taking half of the x coefficient and squaring it %28%281%2F2%29%2A%281%2F2%29%29%5E2=1%2F16
4%28x%5E2%2B%281%2F2%29%2Ax%2B1%2F16%29=3%2B4%2F16add that value to both sides (remember the 4 was factored out, so the complete value should be 4/16 or 1/4)
4%28x%5E2%2B%281%2F2%29%2Ax%2B1%2F16%29=3%2B1%2F4The left side of the equation then becomes 4(x+1/4)^2 (because if it's foiled it becomes 4%28x%5E2%2B%281%2F2%29%2Ax%2B1%2F16%29 again).
4%28x%2B1%2F4%29%5E2=12%2F4%2B1%2F4Simplify right side
4%28x%2B1%2F4%29%5E2=13%2F4
4%28x%2B1%2F4%29%5E2=13%2F4Subtract 13/4 from both sides
%28cross%284%29%2A%28x%2B1%2F4%29%5E2%29%2Fcross%284%29=%2813%2F4%29%2F4Now you can solve for x by first dividing each side by 4
sqrt%28%28x%2B1%2F4%29%5E2%29=sqrt%2813%2F16%29Then take the square root of both sides
x%2B1%2F4=0%2B-sqrt%2813%2F16%29(ignore the zero before the plus/minus)
x%2B1%2F4=0%2B-sqrt%2813%2F16%29finally subtract 1/4 from each side
x=0%2B-sqrt%2813%2F16%29-1%2F4remember the square root of a number is both positive and negative
x=0%2B-sqrt%2813%29%2F4-1%2F4 Add numerators over common denominator
x=%280%2B-sqrt%2813%29-1%29%2F4
So x=%28sqrt%2813%29-1%29%2F4 and x=%28-sqrt%2813%29-1%29%2F4
or in decimal form x=0.6514 and x=-1.1514
Note: the completed square can be verified if you graph both 4x%5E2%2B2x-3=0 and 4%28x%2B1%2F4%29%5E2-13%2F4=0 together. Set them up in y form (ex y=4x%5E2%2B2x-3) and they should both be the same graph. Hope this helps.