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)   (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 to standard form by dividing both sides by 2:
We have: . What we want to do now is to change this equation to a complete square . How can we find out values of somenumber and othernumber that would make it work?
Look at : . Since the coefficient in our equation that goes in front of x is 4, we know that 4=2*somenumber, or . So, we know that our equation can be rewritten as , 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 is equivalent to our original equation .


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

, or .
So, the equation converts to , or .

Our equation converted to a square , equated to a number (6.5).

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


, or






Answer: x=0.549509756796392, -4.54950975679639.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=104 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.549509756796392, -4.54950975679639. Here's your graph:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!



Take of the coefficient
of the x term, square it and add
it to both sides
----------------------------




Take the square root of both sides


and also:

---------------------------
Check my math carefully
Plug either answer back into the
original equation and solve

Answer by lwsshak3(11628)   (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
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