solving equation

Question

what number must be added to the following expression in order to complete the square?

Answer 1

I don't see an equation.  However, if your equation is in the form:  1x² + bx  = 0, in order to make sure the equation is a perfect square, divide b by 2, square it, and add to both sides.

 

Example:  x² + 6x = 0,  b = 6, b/2 = 6/2 = 3,  so (b/2)² = 3² = 9.

 

So add 9 to both sides => x² + 6x + 9 = 9,  and (x + 3)² = 9.

 

Another example:  3x² - 15x - 12 = 0;  divide by 3:  x² - 5x - 4 = 0;  add 4: x² - 5x = 4;

 

Take 1/2 of -5, square it, and add to both sides:  x² - 5x + (25/4) = 4 + (25/4)

 

This becomes:  (x - (5/2))² = (16/4) + (25/4) => (x-(5/2))² = 41/4.

 

I hope this helps.