Question

Solve by completing the square method - 4x²+12x-5

Answer 1

Follow these steps:

- 4x²+12x-5

1) Set the constant in the first term equal to 1 by dividing by -4:

x²-3x+5/4

3) Take 1/2 the second term constant, square it, and add it subtract it.

x²-3x+9/4-9/4+5/4

4) Note that the expression x²+3x+9/4 can be factored as a square

x²-3x+9/4 -9/4+5/4= (x-3/2)(x-3/2)-9/4+5/4 = (x-3/2)^2-4/4

= (x-3/2)^2-4/4

= (x-3/2)^2-1

5) Note that the expression (x-3/2)^2-1 can be factored as it's a difference of squares

= {(x-3/2)-1}{(x-3/2)+1}

= (x-5/2)(x-1/2)

Answer: (x-5/2)(x-1/2)

Hope this help!