How do you solve x^2+8x-2=0x2+8x−2=0 using completing the square?
3 Answers
Solution:
Explanation:
Solution:
Take the second coefficient, divide it by 2, and square it, to complete the square, and obtain the solutions:
Explanation:
To complete the square, take the second coefficient (the one next to the
In this case, that would be
Add this number to both sides of the original equation:
This gives us 2 possible solutions:
Explanation:
"add 2 to both sides"add 2 to both sides
x^2+8x=2x2+8x=2
"add "(1/2"coefficient of the x-term")^2" to both sides"add (12coefficient of the x-term)2 to both sides
x^2+2(4)x color(red)(+16)=2color(red)(+16)x2+2(4)x+16=2+16
(x+4)^2=18(x+4)2=18
color(blue)"take the square root of both sides"take the square root of both sides
sqrt((x+4)^2)=+-sqrt18larrcolor(blue)"note plus or minus"√(x+4)2=±√18←note plus or minus
x+4=+-sqrt18=+-sqrt(9xx2)=+-3sqrt2x+4=±√18=±√9×2=±3√2
"subtract 4 from both sides"subtract 4 from both sides
x=-4+-3sqrt2larrcolor(red)"exact values"x=−4±3√2←exact values
x~~-8.24" or "x~~0.24" to 2 dec. places"x≈−8.24 or x≈0.24 to 2 dec. places