Question 1206854
equation to be solved is 2x^2 - 9x + 5.


set the equation equal to 0 to get 2x^2 - 9x + 5 = 0


divide both sides of the equation by 2 to get a coefficient of 1 in the x^2 term.


you will get x^2 - 9/2 * x + 5/2 = 0


subtract 5/2 from both sides of the equation to get x^2 - 9/2 * x = -5/2


complete the squares for x^2 - 9/2 * x as shown below:


(x - 9/4)^2 - 81/16 = -5/2


you took half of the constant term of -9/2 to get -9/4 and you squared -9/4 to get 81/16.


add 81/16 to both sides of the equation to get (x - 9/4)^2 = -5/2 + 81/16.


take the square root of both sides of the equation to get:


(x - 9/4) = plus or minus sqrt(-5/2 + 81/16).


solve for x to get:


x = 9/4 + sqrt(-5/2 + 81/16) or x = 9/4 - sqrt(-5/2 + 81/16).


the result will be:


x = 3.850781059 or x = .6492189406.


i used a the quadratic equation solve at <a href = "https://www.mathsisfun.com/quadratic-equation-solver.html" target = "_blank">https://www.mathsisfun.com/quadratic-equation-solver.html</a> to get the same answer.


here's a decent reference on how to solve a quadratic equation by using the completing the squares method.


<a href = "https://www.purplemath.com/modules/sqrquad.htm" target = "_blank">https://www.purplemath.com/modules/sqrquad.htm</a>


if you have any questions or you need further help on this, let me know.


theo