SOLUTION: Can you help me solve this equation 2x^2+8x-7=-2 by completing the square? I got this x+4=+or- square root of 7/2.

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Question 911737: Can you help me solve this equation 2x^2+8x-7=-2 by completing the square? I got this x+4=+or- square root of 7/2.
Found 3 solutions by richwmiller, josmiceli, lwsshak3:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics
Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert 2x%5E2%2B8x%2B-5=0 to standard form by dividing both sides by 2:
We have: 1x%5E2%2B4x%2B-2.5=0. What we want to do now is to change this equation to a complete square %28x%2Bsomenumber%29%5E2+%2B+othernumber. How can we find out values of somenumber and othernumber that would make it work?
Look at %28x%2Bsomenumber%29%5E2: %28x%2Bsomenumber%29%5E2+=+x%5E2%2B2%2Asomenumber%2Ax+%2B+somenumber%5E2. Since the coefficient in our equation 1x%5E2%2Bhighlight_red%28+4%29+%2A+x%2B-2.5=0 that goes in front of x is 4, we know that 4=2*somenumber, or somenumber+=+4%2F2. So, we know that our equation can be rewritten as %28x%2B4%2F2%29%5E2+%2B+othernumber, and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that %28x%2B4%2F2%29%5E2+%2B+othernumber is equivalent to our original equation 1x%5E2%2B4x%2Bhighlight_green%28+-2.5+%29=0.


The highlighted red part must be equal to -2.5 (highlighted green part).

4%5E2%2F4+%2B+othernumber+=+-2.5, or othernumber+=+-2.5-4%5E2%2F4+=+-6.5.
So, the equation converts to %28x%2B4%2F2%29%5E2+%2B+-6.5+=+0, or %28x%2B4%2F2%29%5E2+=+6.5.

Our equation converted to a square %28x%2B4%2F2%29%5E2, equated to a number (6.5).

Since the right part 6.5 is greater than zero, there are two solutions:

system%28+%28x%2B4%2F2%29+=+%2Bsqrt%28+6.5+%29%2C+%28x%2B4%2F2%29+=+-sqrt%28+6.5+%29+%29
, or

system%28+%28x%2B4%2F2%29+=+2.54950975679639%2C+%28x%2B4%2F2%29+=+-2.54950975679639+%29
system%28+x%2B4%2F2+=+2.54950975679639%2C+x%2B4%2F2+=+-2.54950975679639+%29
system%28+x+=+2.54950975679639-4%2F2%2C+x+=+-2.54950975679639-4%2F2+%29

system%28+x+=+0.549509756796392%2C+x+=+-4.54950975679639+%29
Answer: x=0.549509756796392, -4.54950975679639.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B8x%2B-5+=+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%2A2%2A-5=104.

Discriminant d=104 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+104+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+104+%29%29%2F2%5C2+=+0.549509756796392
x%5B2%5D+=+%28-%288%29-sqrt%28+104+%29%29%2F2%5C2+=+-4.54950975679639

Quadratic expression 2x%5E2%2B8x%2B-5 can be factored:
2x%5E2%2B8x%2B-5+=+2%28x-0.549509756796392%29%2A%28x--4.54950975679639%29
Again, the answer is: 0.549509756796392, -4.54950975679639. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B8%2Ax%2B-5+%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+2x%5E2+%2B+8x+-+7+=+-2+
+2x%5E2+%2B+8x+=+5+
+x%5E2+%2B+%288%2F2%29%2Ax+=+5%2F2+
Take +1%2F2+ of the coefficient
of the x term, square it and add
it to both sides
----------------------------
+x%5E2+%2B+4x+%2B+%284%2F2%29%5E2+=+5%2F2+%2B+%28+4%2F2%29%5E2+
+x%5E2+%2B+4x+%2B+4+=+5%2F2+%2B+8%2F2+
+x%5E2+%2B+4x+%2B+4+=+13%2F2+
+%28+x+%2B+2+%29%5E2+=+13%2F2+
Take the square root of both sides
+x+%2B+2+=+sqrt%28+13%2F2+%29+
+x+=+%28+-4+%2B+sqrt%2813%29+%29+%2F+2+
and also:
+x+=+%28+-4+-+sqrt%2813%29+%29+%2F+2+
---------------------------
Check my math carefully
Plug either answer back into the
original equation and solve

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Can you help me solve this equation 2x^2+8x-7=-2
***
2x^2+8x-7=-2
2(x^2+4x+4)-8-5=0
2(x+2)^2=13
2(x+2)^2=13
(x+2)^2=13/2
x+2=±√(13/2)
x=-2±√(13/2)
x=-4.55
or
x=0.55