Solve by completing the square x2 + 8x – 2 = 0 show all work

Step-by-step explanation:

Begin by transferring the 2 to the right.

x^2 + 8x = 2

Take 1/2 of 8 (which is 4) and square it. (that would make 16).  Add that to both  sides of the expression

x^2 + 8x + 16 = 2 + 16             Complete the square on the left

(x + 4)^2 = 18                           Take the  square root of both sides.

sqrt(x + 4)^2 = sqrt(18)             Factor 18

sqrt(x + 4)^2 = sqrt(2 * 3 * 3)   Take 3 from under the root sign. The other 3 is discarded.

sqrt(x + 4)^2 = 3* sqrt(2)          Take the sqrt of the binomial on left.

x + 4 = +/- 3 * sqrt(2)                      Subtract 4 from both sides

x = - 4 +/- 3*sqrt(2)                    This is one answer. Find the value of 3*sqrt(2)

x = - 4 +/-  4.2426                      

x1 = -8.2426

x2 = -0.2426

If you have choices, please list them.

I've listed a graph so that you can see that the answers for the roots are correct. The graph was made by using y = x^2 + 8x - 2 and recording the points where y = 0

just sum

10 + 10 = 20

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct