SOLUTION: Use the quadratic formula x^2+8x+7=0 and x^2+12m+11=0

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Question 30224: Use the quadratic formula
x^2+8x+7=0
and
x^2+12m+11=0
Found 3 solutions by checkley71, sdmmadam@yahoo.com, atif.muhammad:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
X~2+8X+7=0. Find two factors that add up to 8 seeing as both the X term and the number are positive. Thus the factors are +7 & +1 or(X+7)(X+1)=0.

X~2+12X+11=0. Find two factors that again add up to 12 as both the X tem and the number are positive. rhus the factors are +11 & +1 or (X+11)(X+1)=0.

Answer by sdmmadam@yahoo.com(530) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+8x+7=0 ----(1)
x^2+(7x+x)+7=0 (splitting the middle term into two parts whose sum is 8x and their product is the product of the square term and the constant term)
(x^2+7x)+(x+7)=0 (additive associativity)
x(x+7)+1(x+7) = 0
xp+ p = 0 where p = (x+7)
p(x+1) = 0
(x+7)(x+1) = 0
(x+7) =0 gives x = -7
(x+1) =0 gives x = -1
Answer: x = -1 and x = -7
Verification: x=-1 in (1) gives
LHS = x^2+8x+7 = 1-8+7 = 0 = RHS
x=-7 in (1) gives
LHS = x^2+8x+7 = 49-56+7 = 0 = RHS
Hence our values are correct
The second problem should be
x^2+12x+11=0
Similar to the above
x^2+12x+11=0
(x+11)(x+1) = 0 (sum is 12 and the product is 11 and so the quantities are
11 and 1)
(x+11) =0 gives x = -11
(x+1) =0 gives x = -1
Answer: x = -1 and x = -11
Verification: x=-1 in (1) gives
LHS = x^2+12x+11 = 1-12+11 = 0 = RHS
x=-11 in (1) gives
LHS = x^2+12x+11 = 121-132+11 = 0 = RHS
Hence our values are correct







Answer by atif.muhammad(135) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B7+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%288%29%5E2-4%2A1%2A7=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+36+%29%29%2F2%5C1+=+-1
x%5B2%5D+=+%28-%288%29-sqrt%28+36+%29%29%2F2%5C1+=+-7

Quadratic expression 1x%5E2%2B8x%2B7 can be factored:
1x%5E2%2B8x%2B7+=+1%28x--1%29%2A%28x--7%29
Again, the answer is: -1, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B7+%29



Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B12x%2B11+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2812%29%5E2-4%2A1%2A11=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+-1
x%5B2%5D+=+%28-%2812%29-sqrt%28+100+%29%29%2F2%5C1+=+-11

Quadratic expression 1x%5E2%2B12x%2B11 can be factored:
1x%5E2%2B12x%2B11+=+1%28x--1%29%2A%28x--11%29
Again, the answer is: -1, -11. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B12%2Ax%2B11+%29