Solve by completing the square x2 + 8x + 2 = 0?

Question

I have been trying to figure out how to do this for over an hour and I keep coming up with the wrong answer because the check never comes out right. If you could please show the work so I will know how to do it in the future.

Answer 1

Completing the square

x² + 8x + 2 = 0

x² + 8x + 2 - 2 = 0 - 2

x² + 8x = - 2

x² + 8x +_____ = - 2 +_____

x² + 8x + 16 = - 2 + 16

(x + 4)(x + 4) = 14

(x + 4)² = 14

(√x + 4)² = ± √14

x + 4 = ± 3.741657387

x + 4 - 4 = - 4 ± 3.741657387

x = - 4 ± 3.741657387

- - - - - - - - - --

Solving for +

x = - 4 + 3.741657387

x = - 0.258342613

- - - - - - - - - -

Solving for -

x = - 4 - 3.741657386

x = - 7.741657386

- - - - - - - - -s-

Answer 2

The first step in "COMPLETING THE SQUARE" is to make sure the coefficient of x² is 1. In this case, the coefficient of x² is 1 and so we do not need to make the coefficient 1.

x² + bx + c = 0

To complete the square you divide 'b' [ie. the coefficient of x]by 2 and square the entire bracket (ie [b/2]² ) and add this into your equation.

If you are adding a number to your equation you also need to subtract it so the equation still equals the same thing. And so if you add [b/2]² to your equation you also need to minus
[b/2]² from the equation.

x² + bx + [b/2]² - [b/2]² + c = 0
and therefore the answer will be:
(x + [b/2])² - [b/2]² + c = 0

And so to complete the square for the equation x² + 8x + 2 = 0
x² + 8x + [8/2]² - [8/2]² + 2 = 0
x² + 8x + [4]² - [4]² + 2 = 0
(x + 4)² - [4]² + 2 = 0
(x + 4)² - 14 = 0

To solve this equation we now want to find what x is equal to, and so we want to get x by it self in order to find what x s equal to.
(x + 4)² - 14 = 0
(x + 4)² = 14
x + 4 = ± √14
x = -4 ± √14 __ __
Therefore x = -4 + √14 OR x = -4 - √14

Hope this helps =]

Answer 3

Step 1: Make sure the coefficient of x² is 1. In this case, it already is.

x² + 8x + 2 = 0

Step 2: Bracket x and HALF the coefficient of x and square the entire bracket.

(x + 4)²

Step 3: From that, subtract HALF the square of the coefficient of x.

(x + 4)² - 4²

Step 4: Simplify the equation. Note that the +2 comes from your original equation.

(x + 4)² - 4² + 2 = 0
(x + 4)² - 14 = 0

Step 5: Solve the equation.

(x + 4)² - 14 = 0
(x + 4)² = 14
x + 4 = ± √14
x = -4 + √14 OR x = -4 - √14

Answer 4

Yo can solve this by using the method that makes the coeeficient of x^2 as 1. Since it is already one, we proceed

x^2 + 8x + 2 = 0
(x)^2 + 2(x)(4) + (4)^2 - (4)^2 + 2 = 0
(x + 4)^2 - (4)^2 + 2 = 0
(x + 4)^2 + 2 - 16 = 0
(x + 4)^2 - 14 = 0
(x + 4)^2 = 14
x + 4 = +/- √14
x = -4 +/- √14

x = -4 + √14 (or) x = -4 - √14 are the solutions

Answer 5

x2 + 8x + 2 = 0
x2 + 8x = -2 (removing the constant term from L.H.S)
(1/2 * co - efficient of x )2
=(1/2 * 8)2
=(4)2
=16
Add 16 on both sides,
x2 + 8x +16 = -2 + 16
(x + 4)2 = 14
Tke square root on both sides,
x + 4 = + or - ,/14
x = + or - ,/14 - 4
Therefore
x =,/14 - 4 or x = -,/14 - 4

Answer 6

(x² + 8 x + 16) - 16 + 2 = 0
(x + 4)² = 14
(x + 4) = ± √14
x = - 4 ± √14

Answer 7

x2 + 8x + 2 = 0
Removing constant term from the L.H.S
x2 + 8x = -2
The missing last term of L.H.S
(8x)2/4x2 = 64x2/4x2
= 16
add 16 to both sides
x2 + 8x +16 = -2 + 16
or
(x+4)2 = 14
extracting square root of both sides
x+4 = /14 , x+4 = -/14
x = /14 -4 , x = -/14 -4

Answer 8

x^2 + 8x + 2 = 0
x^2 + 8x + 16 - 14 = 0
(x + 4)^2 = 14
x + 4 = +/- sqrt(14)
x = -4 +/- sqrt(14)

Answer 9

x^2 + 8x + 2 = 0

ADD +16 TO COMPLETE A RATIONALE FACTOR, BUT THEN, SUBTRACT 16 SO WE ELIMINATE THE 16 WE ADDED.

x^2 + 8x + (16 - 16) + 2 = 0

(x^2 + 8x + 16) - 16 + 2 = 0

(x + 4)^2 - 16 + 2 = 0

(x + 4)^2 - 14 = 0

(x + 4)^2 = 14

SQRT((x + 4)^2) = SQRT(14)

(x + 4) = SQRT(14)

x = SQRT(14) + 4

OR

x = -(SQRT(14)) + 4

Answer 10

for the equation ax^2+bx+c=0
x=[-b+-sqrt(b^2-4ac)]/2a

here a=1, b=8, c=2
x=[-8+-sqrt(64-8)]/2
x=[-8+-2sqrt(14)]/2
x=-4+sqrt(14) or -4-sqrt(14)

Another method:
x^2+2*4x+4^2-14=0
(x+4)^2-[sqrt(14)]^2=0
(x+4+sqrt 14)(x+4-sqrt 14)=0.....since a^2-b^2=(a+b)(a-b)
Either (x+4+sqrt 14)=0 then x= -4-sqrt 14
or (x+4-sqrt 14)=0 then x= -4+sqrt 14