SOLUTION: 2x(x+1)=7

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Question 343890: 2x(x+1)=7
Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2x%28x%2B1%29=7
2x%5E2%2B2x-7=0
Use the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A2%2A%28-7%29+%29%29%2F%282%2A2%29+
x+=+%28-2+%2B-+sqrt%28+4%2B56%29%29%2F4+
x+=+%28-2+%2B-+sqrt%28+60+%29%29%2F4+
x+=+%28-2+%2B-+2sqrt%28+15+%29%29%2F4+
highlight%28x+=+%28-1+%2B-+sqrt%28+15+%29%29%2F2%29+

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
NEED TO KNOW:
TYPE OF EQUATION NEEDED TO USE THE QUADRATIC FORMULA TO SOLVE THE PROBLEM
ax%5E%282%29%2Bbx%2Bc+=0
2x(x+1)=7
DISTRIBUTE AND SIMPIFY
2X%5E%282%29%2B2X=7
2X%5E%282%29%2B2X-7=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B2x%2B-7+=+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=%282%29%5E2-4%2A2%2A-7=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+60+%29%29%2F2%5C2+=+1.43649167310371
x%5B2%5D+=+%28-%282%29-sqrt%28+60+%29%29%2F2%5C2+=+-2.43649167310371

Quadratic expression 2x%5E2%2B2x%2B-7 can be factored:
2x%5E2%2B2x%2B-7+=+2%28x-1.43649167310371%29%2A%28x--2.43649167310371%29
Again, the answer is: 1.43649167310371, -2.43649167310371. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2%2Ax%2B-7+%29