Urgent - Solve the equation by completing the square.?

Question

I received help with the others but I can't figure this one out :

Solve the equation by completing the square.
-7x^2 - 10x + 3 = 0

Answer 1

Solve for x by completing the square.

-7x^2 - 10x + 3 = 0

7x² + 10x = 3
x² + (10/7)x = 3/7
x² + (10/7)x + (5/7)² = 3/7 + (5/7)²
(x + 5/7)² = 3/7 + 25/49 = (21 + 25)/49 = 46/49

Take the square root of both sides.

x + 5/7 = ±√(46/49) = ±√46 / 7

x = (-5 ± √46) / 7

This answer agrees with the result you would get solving the quadratic equation in the usualy way.

Answer 2

-7x^2 - 10x + 3 = 0, move number to right

-7x^2 - 10x = -3, mult both sides be -1 or

7x^2 +10x = 3, factor-out the 7 or

7(x^2 +10/7 x) = 3, div by 7
(x^2 +10/7 x) = 3/7, complete square

(x^2 +10/7 x + (10/14)^2 ) = 3/7 + (10/14)^2, note we add same thing to both sides

(x +10/14)^2 = 3/7 + (10/14)^2, clean-up right side
(x +10/14)^2 = 3/7 + (5/7)^2, clean-up some more
(x +10/14)^2 = 3/7 + 35/49
(x +10/14)^2 = 21/49 + 35/49
(x +10/14)^2 = 56/49, take sqrt, clean up left
x +10/14 = + - sqrt(56/49), clean-up left and right
x + 5/7 = + - sqrt(56)/7

x = (- 5/7) + - sqrt(56)/7 , note there are two answers.

Answer 3

--7x^2 --10x +3 = 0
=> 7x^2 + 10x = 3
=> x^2 + 2(5/7)x + (5/7)^2 = 3/7 + (5/7)^2
=> (x + 5/7)^2 = 46/49
=> x + 5/7 = (sqrt46)/7 or --(sqrt46)/7
=> x = --5/7 + (sqrt46)/7 or x = --5/7 +
(sqrt46)/7

Answer 4

divide by -7 first

x^2 +10/7x = 3/7

x^2 + 10/7x + (5/7)^2 = 3/7 + (5/7)^2
(x+5/7)^2 = 46/49
x+5/7 = sqr(46)/7
x = -5/7 + sqr(46)/7 = 0.255
or -5/7 - sqr(46)/7 = -1.68

The main thing once you have x^2 +bx = c
add (b/2)^2 on both side to get a perfect square with
(x+b/2). then take the sq root on both side and you have the two roots of a quad eq.