Quad. Formula is wrong! compared with completing the square?

Question

Even using the formula I can't even get the right anwser this is none sense.
-b+/-√b²-4ac /2a

Prob.
-x²-8x+3=0

Solving.
x²+8x-3=0
-8+/-√64-4*1*-3/2

x=-8+/-√76/2

The anwser is totally wrong, how useless the formula is...

Complete the square.

(x+8/2)²-64/4=-3 +64/4
(x+8/2)²=52/4
(x+8/2)=2+/-√13/2
X=-8+/-√13/2

Answer 1

You're missing parentheses, it's:

(-b+/-√(b² - 4ac)) / 2a

The "-b" part is divided by "2a" as well, so instead of -8, it should be -4.

For your equation, after multiplying by -1 so that the coefficient of x^2 is positive: a = 1, b= 8, c=-3

{-(8) +/- √[(8)^2 - 4*1*(-3)]}/2*(1) =
{ -8 +/- √[64 + 12] } / 2 =
-4 +/- √(76)/2 =
-4 +/- √(19)

Since √(76)/2 = √(4*19)/2 = 2√(19)/2 = √(19)

====================

Completing the square:

x^2 + 8x - 3 = 0
x^2 + 8x = 3
x^2 + 8x + 16 = 3 + 16
(x + 8/2)^2 = 3 + 16
(x + 4)^2 = 19
x + 4 = +/- √(19)
x = -4 +/- √(19)

I get the same answer either way.

Answer 2

x² + 8x - 3 = 0
Formula
x = [- 8 ± √(64 + 12)] / 2
x = [- 8 ± √76 ] / 2
x = [- 8 ± 2√19] / 2
x = - 4 ± √19

Completing the square
x² + 8x = 3
x² + 8x + 16 = 3 + 16
(x + 4)² = 19
(x + 4) = ±√19
x = - 4 ± √19

Answer 3

Completing the square:
x²+8x-3=0
Add 19 to both sides:
x²+8x-3+19=0+19
x²+8x+16=19
(x+4)² = 19
x + 4 = +/- √19
x = -4 +/- √19

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Quadratic-solving equation:

{ -b +/- SQRT[ b² - (4*a*c) ] } / 2a

(don't forget the 2 in the denominator)

You have:
x²+8x-3=0

a=1 b=8 c=-3

{ -8 +/- SQRT[ 8² - (-12) ] } / 2
{-8 +/- SQRT(64+12)} / 2
Distribute the division by 2:
-8/2 +/- (1/2)*SQRT(76)
76 = 4*19
-4 +/- SQRT(4*19)
the square root of a product is the product of roots:
-4 +/- (1/2)*SQRT(4)*SQRT(19)
SQRT(4) is 2
-4 +/- (1/2)*2*SQRT(19)
-4 +/- SQRT(19)

Same as above.

Answer 4

You made a mistake after.. x=-8+/-√76/2



√76 --> becomes --> √2 * 2 * 19--> which becomes ->> 2√19

so...

-8+/-2√19/2

-8 +/- √19

Answer 5

winding up the sq.: - x² + 8x + sixteen = 10 + sixteen (x + 4)² = 26 x + 4 = ± ?26 x = ±?26 - 4 = - 4 ±?26 Quadratic formulation: - x = { - 8 ± ?( sixty 4 + 40) } / 2 x = { - 8 ± ?104 } / 2 x = { - 8 ±?(4 x 26) } / 2 x = {- 8 ± 2?26 } / 2 x = - 4 ±?26

Answer 6

Actually the equation doesn't do anything but solve the quadratic equation. It is correct. Based on the discriminant it could either yield two real solutions, one real solution, or two non-real conjugate complex solutions.

I got -4 +/- √19 which is the same answer as yours just simplified. And using simple plug in to the original quadratic, you will find that the answers are both correct. You messed up your math on completing the square.