Question 981399: Complete the square on the following quadratic
x2+14x+9=0
what value is added to both sides of the equation.
Found 3 solutions by Boreal, richwmiller, rothauserc:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x^2+14x+9=0
x^2+14x=-9
take half of the x term and square it, adding that number to both sides of the equation.
x^2+14x+49= -9+49
(x+7)^2=40
x+7= sqrt (40)=+/- 2 sqrt 10
x= -7 +/- 2 sqrt (10)
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 1:
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 14, we know that 14=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 9 (highlighted green part).
 , or  .
So, the equation converts to  , or  .
Our equation converted to a square  , equated to a number (40).
Since the right part 40 is greater than zero, there are two solutions:
, or
Answer: x=-0.675444679663241, -13.3245553203368.
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Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! x^2 + 14x + 9 = 0
subtract 9 from both sides of =
x^2 + 14x = -9
divide x coefficient by 2 and square it, then add 49 to both sides of =
x^2 + 14x + 49 = 40
factor polynomial
(x + 7) * (x + 7) = 40
take square root of both sides of =
x + 7 = 2 * square root of 10
x = 2 * square root(10) - 7 = −0.68
x = 2 *(-square root(10)) - 7 = −13.32
x = −0.68 or x = −13.32
NOTE. we added 49 to both sides of the equation
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