You can put this solution on YOUR website! Solve by completing the square: First, subtract 5x from both sides of the equation. Complete the square in the x-terms by adding the square of half the x-coefficient (that's to both sides of the equation. Simplify. Now take the square root of both sides. ...and , of course, the right side has a + or - in front. Now add 5/2 to both sides. +or-
You can put this solution on YOUR website! Solve by completing the square.
x^2=5x+2
The golden rule for completing the square method:
Keep the square term and the term in x on the LHS.
When the coefficient of x^2 is 1 and the term in x is positive, then
think of your perfect square in the form
[x+(1/2)times the coefficient of the term in x]^2
Then expand using (a+b)^2 formula which gives apart from your two terms on the left an additional quantity that is a constant.
And if coefficient of x^2 is 1 and the term in x is negative, then
think of your perfect square in the form
[x-(1/2)times the coefficient of the term in x]^2
Then expand using (a-b)^2 formula which gives apart from your two terms on the left an additional quantity that is a constant.
It is this constant that you have to add to both the sides. You have a perfect square on theLHS and on the RHS you have a sum of the given constant and the constant you have added.
Simplify the sum on the right.
Then take square root.
Do not forget to give (+ or -)sign to the root on the right.
Transfer the constant term from the left to the right.
You get two answers:
x= (the transfered constant+the rootwith the positive sign)
and x = (the transfered constant+the root with the negative sign))
x^2=5x+2
x^2-5x = 2
We have (x-5/2)^2 = x^2-5x +25/4
Therefore we need 25/4 for the LHS to become a perfect square.
Adding 25/4 to both the sides,
x^2-5x +25/4= 2+25/4
That is (x-5/2)^2 = (8+25)/4
(x-5/2)^2 = (33)/4
Taking sqroot
(x-5/2)=+ or -)sqroot(33/4)
x = [5/2+(or -)sqroot(33/4)]= [5/2+(or -)(1/2)sqroot(33)]
That is x = (5/2)+(1/2)[(33)^(1/2)]
And x = (5/2)-(1/2)[(33)^(1/2)]
OR x = [5+ sqrt(33)]/2 and x = [5- sqrt(33)]/2
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