It looks like you’re solving the equation by completing the square.
The approach used seems to be: Step 1: Make the first term x^2 not 2x^2, by dividing every term by 2.
x^2 + 1/2 x - 2=0 Note here that because the computer had “+” before the second box in the first line, you needed to put “-2” instead of 2 to keep the sign correct.
Step 2: Move that -2 to the other side and then figure out what you’re going to add to the right side to complete the square. The way you do this is you take the “b” value from “bx” and divide it by 2 and square it. Divide b by 2: 1/2 ÷ 2 = 1/2 • 1/2 = 1/4 Square that: (1/4)^2 = 1/16 So you need to add 1/16 to both sides.
The final step is to factor the left side and add the numbers on the right side. Left side: x^2 + 1/2x + 1/16 = (x+1/4)^2. The 1/4 can be found either by dividing the “b” by 2 or taking the square root of 1/16. Both give you 1/4. You can always double check your work by FOILing out (x+1/4)^2 as (x+1/4)(x+1/4) and making sure you get used 1/4 correctly.
On the right side, 2 + 1/4 = 2/1 + 1/4 = 8/4 + 1/4 = 9/4 You need to find a common denominator to add them.
The above process will always work. How messy it is totally depends on the numbers involved.
