How would you answer 2x squared -15x + 7 in completing the square format?

Answer 1

2 x ² - 15 x + 7
2 [ x² - (15/2) x + 7/2 ]
2 [ (x² - (15/2) x + 225/16) - 225/16 +7/2 ]
2 [ (x - (15/2) x + 225/16) - 169/16 ]
2 [ ( x - (15/4) ) ² - (13/4) ² ]

Answer 2

In other words...complete the square in the function:
2x^2 - 15x + 7

We want it to look like (x + a)^2 + b

To complete the square first factor out a 2 to make the x^2 term have a coefficient of 1.

2(x^2 - 15/2x + 7/2)

Now divide the x term by 2.
-15/2 divided by 2 = -15/4
Now square that.
(-15/4)^2 = (-15/4)(-15/4) = 225/16

We can add this into the original function and make a perfect square binomial. But we can't just add a value in or we have changed the original function. We have to subtract out what we add in.

2(x^2 - 15/2x + 225/16 - 225/16 + 7/2)
= 2[(x^2 - 15/2x + 225/16) - 225/16 + 56/16]
= 2[(x^2 - 15/2x + 225/16) - 169/16]
The value in the parenthesis is a perfect square. It is (x - 15/4)^2. We want our formula to look like that so replace what is in parenthesis above with this.
= 2[(x - 15/4)^2 - 169/16]
Finally distribute...
= 2(x - 15/4)^2 - 169/8

From the original function we see if we plug in zero we should get 7.

2(0 - 15/4)^2 - 169/8
= 2(225/16) - 169/8
= 225/8 - 169/8
= 56/8
=7
This is a nice way to check your answer.

Answer 3

2x^2 - 15x + 7 = 0 to end the sq., you are going to be able to desire to manage the equation. the 1st step - Get the x^2 by potential of itself. for this reason, divide each little thing by potential of "2". x^2 - (15/2)x + (7/2) = 0 Step 2 - 0.5 the fee of "15/2" which turns into "15/4" Step 3 - sq. this fee. (15/4)^2 = 225/sixteen Step 4 - Now upload 225/sixteen to the two sides and take the "7/2" to the different ingredient. (be conscious: What you do to a minimum of one ingredient, you are going to be able to desire to do to the different ingredient.) x^2 - (15/2)x + (7/2) + (225/sixteen) = 225/sixteen x^2 - (15/2)x + (225/sixteen) = (225/sixteen) - (7/2) Now in view that 225/sixteen is the sq. of 15/4, x^2 - (15/2)x + (225/sixteen) turns into (x - [15/4])(x - [15/4]) So as a result: (x - [15/4])(x - [15/4]) = (225/sixteen) - (7/2) (x - [15/4])(x - [15/4]) = 169/sixteen (x - [15/4])(x - [15/4]) - (169/sixteen) = 0 (x - 3.seventy 5)^2 - (169/sixteen) = 0