SOLUTION: What is x^2+8x+6=0 using the completing the square method

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Question 1059138: What is x^2+8x+6=0 using the completing the square method
Found 3 solutions by josgarithmetic, josmiceli, ikleyn:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
You have a rectangle of area x%5E2%2B8x and the missing square piece, if a piece from the rectangle is appropriately rearranged, is %288%2F2%29%5E2=4%5E2. Add this to both sides of your equation, and simplify, and solve for x.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+%2B+8x+%2B+6+=+0+
+x%5E2+%2B+8x+=+-6+
Take 1/2 of the coefficient of +x+,
square it, and add it to both sides
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+x%5E2+%2B+8x+%2B+%288%2F2%29%5E2+=+-6+%2B+%288%2F2%29%5E2+
+x%5E2+%2B+8x+%2B+16+=+-6+%2B+16+
+%28+x+%2B+4+%29%5E2+=+%28+sqrt%2810%29+%29%5E2+
Take the square root of both sides
+x+%2B+4+=+sqrt%2810%29+
+x+=+-4+%2B+sqrt%2810%29+
and, also, taking the negative square root of +10+,
+x+%2B+4+=+-sqrt%2810%29+
+x+=+-4+-+sqrt%2810%29+
---------------------------
check:
+%28+-4+%2B+sqrt%2810%29+%29%5E2+%2B+8%2A%28+-4+%2B+sqrt%2810%29+%29+%2B+6+=+0+
+16+-+8%2Asqrt%2810%29+%2B+10+-+32+%2B+8%2Asqrt%2810%29+%2B+6+=+0+
+16+%2B+10+-+32+%2B+6+=+0+
+32+-+32+=+0+
+0+=+0+
OK
You can check the other answer

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
What is x^2+8x+6=0 using the completing the square method
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1.  First let us complete the square:

    x%5E2+%2B+8x+%2B+6 = %28x%5E2+%2B+8x+%2B+16%29+-+16+%2B+6 = %28x%5E2+%2B+2%2A4x+%2B+4%5E2%29+-+10 = %28x%2B4%29%5E2+-+10.


2.  Having this, you can re-write the original equation as

    %28x%2B4%29%5E2+-+10 = 0,   or

    %28x%2B4%29%5E2 = 10.

    Take the square root from both sides:

    x + 4 = +/-sqrt%2810%29,  or

    x = -4+%2B-+sqrt%2810%29.

The equation is solved.
The assignment is completed.

On completing the square see the lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Quadratic equations".