Completing the square

Hi, so my homework over the holidays was to complete a practice paper (from the textbook).
Here's the problem: I can't remember how to complete the square!!!
So here's the question:

Show by completing the square that the equation 2x^2=8x-7 has solutions 2√2 +or- 1 / √2

All I know is that I have to start by making it equal to zero, right?
So, 2x^2-8x+7=0 ?

Any help would be greatly appreciated!!
(btw sry I didn't write it all out properly in the question but I'm not used to writing maths stuff on the computer so Idk how to do it... I hope u understand it anyway)

Reply 1

brainmaster

14

since you want to learn completing the square. ..I will give you a general way;

let's take the equation ax^2 + bx + c

now completing the square for this will be;
a [(x + b/2a)^2 - (b/2a)^2] + c

but when we are solving...you don't include the a outside the bracket. so if we were solving the equation ax^2 + bx + c = 0 then that would be;

(X + b/2a)^2 - (b/2a)^2 = -c/a.

now I will go further and solve for x here and you will see what we have at the end :smile:

(X + b/2a)^2 - b^2/4a^2 = -c/a

(X + b/2a)^2 = -c/a + b^2/4a^2

we can wrie the fraction on the RHS as one;

(X + b/2a)^2 = (-4ax + b^2)/4a^2

square root both sides;

x + b/2a = sqrt {b^2 - 4ac}/2a

leave x alone;
x = (-b +- sqrt {b^2 - 4ac})/2a.....And thats the quadratic formula :wink:

that was just a by the way but just remember the formulas at the start (how to arrange the values for completing the square) and the rest will just flow automatically :wink:

let me know if I helped :smile:

Reply 2

Y2_UniMaths

19

https://youtu.be/zKV5ZqYIAMQ this video will help

Reply 3

mikaelalrc

OP

8

Original post by brainmaster

since you want to learn completing the square. ..I will give you a general way;

let's take the equation ax^2 + bx + c

now completing the square for this will be;
a [(x + b/2a)^2 - (b/2a)^2] + c

but when we are solving...you don't include the a outside the bracket. so if we were solving the equation ax^2 + bx + c = 0 then that would be;

(X + b/2a)^2 - (b/2a)^2 = -c/a.

now I will go further and solve for x here and you will see what we have at the end :smile:

(X + b/2a)^2 - b^2/4a^2 = -c/a

(X + b/2a)^2 = -c/a + b^2/4a^2

we can wrie the fraction on the RHS as one;

(X + b/2a)^2 = (-4ax + b^2)/4a^2

square root both sides;

x + b/2a = sqrt {b^2 - 4ac}/2a

leave x alone;
x = (-b +- sqrt {b^2 - 4ac})/2a.....And thats the quadratic formula :wink:

that was just a by the way but just remember the formulas at the start (how to arrange the values for completing the square) and the rest will just flow automatically :wink:

let me know if I helped :smile:

Thank you very much!!!!! I really appreciate it :h: