how to complete the square of these problems step by step

Question

3x²+6x=2x²+40

And 

x²-2x=3

And

x²+10x-3=0

Answer 1

1.  3x²+6x=2x²+40

 

Subtract 2x² from each side:  x² + 6x = 40

 

To have a perfect square, the last term needs to be a perfect square, and to find it, take half of the middle coefficient (in this case,6) and square it, adding the result to both sides.

 

This gives:  x² + 6x + 9 = 40 + 9,  or x² + 6x + 9 = 49.

 

This makes the left half a perfect square:  (x + 3)² = 49

 

Taking the square root of each side:  |x + 3| = 7

 

Removing the absolute value: x + 3 = ±7,  so x + 3 = 7,  and   x + 3 = -7.

 

Therefore x = 4, and x = -10.

 

2. x² - 2x + 1 = 3 + 1 ==> (x - 1)² = 4 ==> |x - 1| = 2 ==> x - 1 = ±2

 

3. x² + 10x = 3;  x² + 10x + 25 = 3 + 25;  (x + 5)² = 28;  x + 5 = ±√28; x = -5 ±2√7

  I Hope this helps.