Solve by Completing the Square

Question

2x^2 - 5x = 6

Answer 1

Hi Ethan,

 

The process for completing the square is as follows:

 

1) Use addition and subtraction to move the constant term to the right and all other terms to the left.
2) Divide each term in the equation by the coefficient of the x^2 term, unless the coefficient is 1.
3) Determine the coefficient of the x term, divide it by two, square it, and add to both sides.
4) Factor the left side as a perfect square.
5) Take the square root of each side and solve for x.

 

Let's do that.

a = 2  so we will divide both sides by 2

2x^2 - 5x = 6 and we get

x^2 - (5/2)x = 3

coefficient of x is -5/2. half of it is -5/2*(1/2) = -5/4

we will add its square to both sides.

 

x^2 - (5/2)x + (-5/4)^2 = 3 + (-5/4)^2

(x - 5/4)^2 = 73/16

take the square root os both sides

(x - 5/4) = ± sqrt(73/16)

x - 5/4 = ± sqrt(73)/4

x = ± sqrt(73)/4 + 5/4

x = (sqrt(73) + 5) / 4  and x = -(sqrt(73) + 5) / 4