Jimmy E. answered • 10/02/14
Tutor
5
(1)
If you want to succeed in math, I am ready to help you
First you want to set the expression equal to zero and keep the x^2 and x terms on the same side: 2x^2 + 5x - 1 = 0, or 2x^2 + 5x = 1.
Next you want to get your leading coefficient to be 1. Therefore we have x^2 + 5/2 x = 1/2.
To complete the square you divide your x coefficient by 2 and square the result--5/2 divided by 2 is 5/4; and 5/4 squared is 25/16.
You add this to both sides of the equation--x^2 + 5/2 x + 25/16 = 1/2 + 25/16 = 8/16 + 25/16 = 33/16.
To simplify the left hand side of the equation as a binomial squared, go back to what we did to divide the original x coefficient by 2. We can rewrite the left hand side as (x + 5/4)^2 = 33/16.
To solve the equation take the square root of each side, so x + 5/4 = +-(sqrt)33/4, or x = -5/4 +-(sqrt)33/4.
