SOLUTION: Good afternoon please help me solve the following equation 2𝑥^2 − 9𝑥 + 5 = 0 Using completing the square method Thank you

Click here to see ALL problems on Equations

Question 1206854: Good afternoon please help me solve the following equation
2𝑥^2 − 9𝑥 + 5 = 0 Using completing the square method
Thank you
Found 2 solutions by Theo, josgarithmetic:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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 https://www.mathsisfun.com/quadratic-equation-solver.html to get the same answer.

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

https://www.purplemath.com/modules/sqrquad.htm

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

theo

Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!

If you were to make a graphical representation, you could arrange the parts so
would appear a missing square piece....

You equation assigned a=2, b=-9, c=5.