solve by completing the square 4 X^2 + 2X – 3 = 0?

Question

solve by completing the square 4 X^2 + 2X – 3 = 0

Answer 1

if you put (2x+1)^2 =4x^2+2x +1

then you can write (2x+1)^2-4 =0

(2x+1-2) (2x+1+2) =0

(2x-1)(2x+3) =0

roots x=1 x=-3

Answer 2

The "key" to polishing off the sq. is to look on the consistent earlier the "x" term So x^2 + 2x - 3. the consistent to pay interest on is two Now, think of roughly what happens once you look at (x + a million)^2 prolonged out, that's x^2 + 2x + a million^2 be conscious the "2" interior the x^a million term So x^2 + 2x desires a "+ a million" to make it a sq. like (x + a million)^2 So, we 0.5 this fee and sq. it to get what we are lacking/ to maintain the equation balanced, we would desire to constantly upload the adverse of the sq. so x^2 + 2x + a million - a million = (x + a million)^2 - a million so x^2 + 2x -3 = 0 ==>x^2 + 2x + a million -a million -3 = 0 ==>(x + a million)^2 -4 = 0 ==> (x + a million)^2 = 4 you're able to do the same element with the different one, however the 1st step is to do away with the "2" in front of the x^2 term: 2x^2 - 3x + a million = 0 ==> x^2 - 3x/2 + a million/2 = 0 ==> (x^2 - 3x/2 + (3/4)^2 - (3/4)^2 + a million/2 = 0 ==> (x -3/4)^2 - 9/sixteen + a million/2 = 0 ==> (x- 3/4)^2 - a million/sixteen = 0 ==> (x - 3/4)^2 = a million/sixteen ==> x - 3/4 = +/- a million/4 ==> x = 3/4 +/- a million/4 ==> x = 3/4 + a million/4 = a million or x = 3/4 - a million/4 = a million/2 = 0.5 so (a million, 0.5) is the respond