Question 252802: Can the following equation be solved by the method "completing the square"
4x^2 – 7x – 2 = 0 Found 2 solutions by ptaylor, Theo:Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! 4x^2 – 7x – 2 = 0 add 2 to each side
4x^2-7x=2 divide each term by 4
x^2-(7/4)x=1/2 take half of the x coefficient and square it and we get 49/64 and add to each side:
x^2-(7/4)x+49/64=32/64+49/64=81/64
(x-7/8)^2=81/64 take square root of each side
x-7/8=+or-9/8
x=7/8+or-9/8
x=-2/8=-1/4
and
x=16/8=2
The answer is "yes"
Hope this helps---ptaylor
all quadratic equations can be solved by completing the squares method. some are easier than others. there are some steps that you have to go through to make the a term in the equation equal to 1.
the standard form of a quadratic equation is ax^2 + bx + c = 0 where:
a = coefficient of the x^2 term.
b = coeficient of the x term.
c = a constant.
here's how your equation is solved using the completing the squares method.
add 2 to both sides of the equation to get:
divide both sides of the equation by 4 to get:
take half of (7/4) to get (7/8)
take (7/8) squared to get (7/8)^2 = (49/64)
your equation becomes:
see bottom for explanation of how this was derived.
take square root of both sides to get:
= +/-
add (7/8) to both sides to get:
+/-
this makes x equal to:
or:
this makes x equal to:
2 or -.25
substitute in original equation to confirm these answers.
original equation is:
when x = 2, equation becomes which becomes 16-14-2 = 0 which becomes 2-2 = 0 which becomes 0 = 0 confirming x = 2 is good.
when x = -.25, equation becomes which becomes .25 + 1.75 - 2 = 0 which becomes 2 - 2 = 0 which becomes 0 = 0 confirming x = -.25 is good.
both answers are good.
your answers are:
x = 2 or x = -.25
bottom:
the equation you want to complete the squares on is:
the coefficient of the x^2 term has to be 1 in order for this method to work.
we divided both sides of the equation by 4 to make that happen and were left with:
completing the squares methods requires we take the square root of where k is a constant.
we do that by taking one half of the b term which is the coefficient of x.
the constant term of k will always be equal to one half of the b term squared.
one half of (7/4) = (7/8)
since the b term is negative, our factor will be:
.
.
since we want to be equal to , we have to subtract (49/64) from to make it equal to
our equation of:
becomes equivalent to:
we add (49/64) to both sides of the equation to get:
