Solve by completing the square of by quadratic equation -84x2 8x-12?

Answer 1

hmm... i don' think you have the completed the question. This one is pretty hard! Solving quadratics can be difficult and ompleting the square is one method for solving a quadratic equation.

Is the equation -84x2-8x-12=0 or -84x2+8x - 12 = 0 or -84x2 = 8x - 12?

If it is the first one:

Factor out the 4:

-4 (21x2 + 2x + 3) = 0

21x2 + 2x + 3 = 0 (divide by 21 each term to both sides)

x2 + (2/21)x + 3/21 = 0 (subtract 3/21 to both sides)

x2 + (2/21)x = -3/21 (add (1/2 of 2/21)2 or (1/21)2 to both sides)

x2 + (2/21)x + (1/21)2 = -3/21 + 1/212

(x + 1/21)2 = -63/212 + 1/212

(x + 1/21)2 = -62/212 (square root to both sides)

x + 1/21 = ± √-62/212

x + 1/21 = ± (i/21)√62 (subtract 1/21 to both sides)

x = -1/21 ± (i/21)√62

x = -1/21 (1 - i√62) or

x = -1/21 (1+ i√62)

If it is the third one:

-84x2 = 8x - 12 (divide by -84 to both sides)

x2 = -(2/21)x + 3/21 (add (2/21)x to both sides)

x2 + (2/21)x = 3/21 (add (1/2 of 2/21)2 or (1/21)2 to both sides)

x2 + (2/21)x + (1/21)2 = 3/21 + 1/212

(x + 1/21)2 = 63/212 + 1/212

(x + 1/21)2 = 64/212 (square root to both sides)

x + 1/21 = ± √64/212

x + 1/21 = ± 8/21 (subtract 1/21 to both sides)

x = -1/21 ± 8/21

x = -1/21 + 8/21 = 7/21 = 1/3 or

x = -1/21 - 8/21 = -9/21 = -3/7