SOLUTION: Find the solutions to: x^2 + 8x=-16 Find the solutions to: x^2-16x= -64 Find the solutions to : x^2+8x+15=0 The sum of the solutions is:

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the solutions to: x^2 + 8x=-16 Find the solutions to: x^2-16x= -64 Find the solutions to : x^2+8x+15=0 The sum of the solutions is:      Log On


   

Question 183494: Find the solutions to: x^2 + 8x=-16
Find the solutions to: x^2-16x= -64
Find the solutions to : x^2+8x+15=0 The sum of the solutions is:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the solutions to: x^2 + 8x=-16
x^2 + 8x + 16 = 0
(x+4)*x+4) = 0
x = -4 a single solution, it's tangent to the x-axis.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B16+=+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%2A16=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%288%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B8x%2B16+=+%28x--4%29%2A%28x--4%29

Again, the answer is: -4, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B16+%29

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Find the solutions to: x^2-16x= -64
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-16x%2B64+=+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=%28-16%29%5E2-4%2A1%2A64=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-16%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B-16x%2B64+=+%28x-8%29%2A%28x-8%29

Again, the answer is: 8, 8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-16%2Ax%2B64+%29

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Find the solutions to : x^2+8x+15=0 The sum of the solutions is:
(x+3)*(x+5) = 0
x = -3, x = -5
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B15+=+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%2A15=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+4+%29%29%2F2%5C1+=+-3
x%5B2%5D+=+%28-%288%29-sqrt%28+4+%29%29%2F2%5C1+=+-5

Quadratic expression 1x%5E2%2B8x%2B15 can be factored:
1x%5E2%2B8x%2B15+=+%28x--3%29%2A%28x--5%29
Again, the answer is: -3, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B15+%29