solve each equation by completing the square. b^2+8b+1+-6?
回答 (8)
2008-06-12 4:47 pm
✔ 最佳答案
I suspect the equation was supposed to be:b^2 + 8b + 1 = -6
If so, subtact 1 from each side:
b^2 + 8b = -7
Take half of the "b" term's coefficient (8b) which is 4, and square it, which is 16. Add this to both sides:
b^2 + 8b + 16 = 9
Factor left side:
(b+4)^2 = 9
Square of both sides, remembering to have a +/- on the right:
b+4 = +/-3
Therefore:
b = -4 +/- 3
b = -7 or -1
2008-06-12 4:46 pm
Did you mean b^2+8b+1 =-6?
If so,
Equation: b^2+8b+1
(b^2+8 b)+1
(b^2+8 b+(8/2)^2)+1-(8/2)^2
bx+8/2)^2+1-64/4
(b+4)^2-60/4
(b+4)^2-15=-6
(b+4)^2=15-6
(b+4)^2=9
(b+4) = +/-3
b= -4 +/-3
b=-4-3 =-7
b=-4 +3 =-1
b=-7,-1
If so,
Equation: b^2+8b+1
(b^2+8 b)+1
(b^2+8 b+(8/2)^2)+1-(8/2)^2
bx+8/2)^2+1-64/4
(b+4)^2-60/4
(b+4)^2-15=-6
(b+4)^2=15-6
(b+4)^2=9
(b+4) = +/-3
b= -4 +/-3
b=-4-3 =-7
b=-4 +3 =-1
b=-7,-1
2008-06-12 8:18 pm
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2008-06-12 5:37 pm
b^2 + 8b+1+-6
b^2+8b+(1-6)=b^2+8b-5
b^2+8b=5
coeff. of b=8
half the coeff.of b=4
square of half the coeff of b=16
add the square of the coeff to both sides
b^2+8b+4^2=5+16
(b+4)^2=21
b+4=Square root of 21
b= -4+4.9 or -4-4.9
b= 0.9 or -8.9
b^2+8b+(1-6)=b^2+8b-5
b^2+8b=5
coeff. of b=8
half the coeff.of b=4
square of half the coeff of b=16
add the square of the coeff to both sides
b^2+8b+4^2=5+16
(b+4)^2=21
b+4=Square root of 21
b= -4+4.9 or -4-4.9
b= 0.9 or -8.9
參考: well i used a calculator
2008-06-12 5:11 pm
b^2 + 8b + 1 = -6
b^2 + 8b + 1 + 6 = 0
b^2 + 8b + 7 = 0
(b + 4)^2 - 9 = 0
(b + 4)^2 = 9
b + 4 = 屉9
b + 4 = ±3
b + 4 = 3
b = 3 - 4
b = -1
b + 4 = -3
b = -3 - 4
b = -7
â´ b = -1 , -7
b^2 + 8b + 1 + 6 = 0
b^2 + 8b + 7 = 0
(b + 4)^2 - 9 = 0
(b + 4)^2 = 9
b + 4 = 屉9
b + 4 = ±3
b + 4 = 3
b = 3 - 4
b = -1
b + 4 = -3
b = -3 - 4
b = -7
â´ b = -1 , -7
2008-06-12 4:57 pm
i believe it is actually b^2+8b+1=-6
b^2+8b+1=-6
Subtract the constant 1,
b^2+8b=-7
Note:
(a+b)^2=a^2+2ab+b^2
so far we have the a^2+2ab part
(b)^2+2(b)(4)=-7
to complete add (4)^2
(b)^2+2(b)(4)+(4)^2=-7+(4)^2
(b+4)^2=-7+16
(b+4)^2=9
square root both sides
b+4=+/-sqrt9
b+4=+/-3
b=-4+/-3
that's 2 solutions:
b=-4-3=-7
and
b=-4+3=-1
{-7,-1}
hope this helped. peace
b^2+8b+1=-6
Subtract the constant 1,
b^2+8b=-7
Note:
(a+b)^2=a^2+2ab+b^2
so far we have the a^2+2ab part
(b)^2+2(b)(4)=-7
to complete add (4)^2
(b)^2+2(b)(4)+(4)^2=-7+(4)^2
(b+4)^2=-7+16
(b+4)^2=9
square root both sides
b+4=+/-sqrt9
b+4=+/-3
b=-4+/-3
that's 2 solutions:
b=-4-3=-7
and
b=-4+3=-1
{-7,-1}
hope this helped. peace
2008-06-12 4:53 pm
b^2+8b+16-21
(b+4)^2 - 21
(b+4)^2 - 21
2008-06-12 4:39 pm
b^2+8b+1+-6
This isn't an equation, doesn't equal anything.
This isn't an equation, doesn't equal anything.
收錄日期: 2021-05-01 10:38:06
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