SOLUTION: Hi, I am really stuck on this one! Can someone please help? I need to solve this by completing the square;
4x^2 - 3x + 1
PLEASE help and explain your steps???
Question 485481: Hi, I am really stuck on this one! Can someone please help? I need to solve this by completing the square;
4x^2 - 3x + 1
PLEASE help and explain your steps???
You can put this solution on YOUR website! the roots on this are imaginary.
here's what the graph looks like.
It doesn't cross the x-axis so it has no real roots.
you can solve it by completing the square but it will have a negative square root.
the equation is 4x^2 - 3x + 1
set it equal to 0 and subtract 1 from both sides of the equation to get:
4x^2 - 3x = -1
divide both sides of the equation by 4 to get:
x^2 - .75x = -.25
take half the .75 to get .375
square half the .75 to get .375^2 = .140625 and then add it to the right side of the equation to get.
(x - .375)^2 = -.25 + .140625
combine like terms to get:
(x - .375)^2 = -.109375
take the square root of both sides of the equation to get:
x - .375 = +/- sqrt(-.109375)
add .375 to both sides of the equation to get:
x = .375 +/- sqrt (-.109375)
Since you cannot take the square root of -.109375 and get a real number, the equation has no roots.
this is confirmed by the graph because, if the equation had real roots, the graph of the equation would have crossed the x-axis.
if you need a tutorial on how to find the roots of an equation by completing the square, check out the following reference. http://www.purplemath.com/modules/sqrquad.htm
