Question 613669: to solve by completing the square, what value should you add to each side of the equation? x^2+20x=-4
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x^2+20x=-4
you take 1/2 the value of the coefficient of the b term and you square it and add it to the other side of the equation.
you start with x^2 + 20x = -4
the standard form of a quadratic equation is:
ax^2 + bx + c = 0
your equation is:
x^2 + 20x = -4
add 4 to both sides to get it into the standard form of:
x^2 + 20x + 4 = 0
that makes:
a = 1
b = 20
c = 4
1/2 of 20 = 10
your equation is x^2 + 20x = -4
after taking 1/2 the coefficient of the b term, you will get:
(x + 10)^2 = -4 + 10^2 which becomes:
(x + 10)^2 = 96
you then take the square root of both sides of this equation to get:
x + 10 = +/- sqrt(96)
you then subtract 10 from both sides of this equation to get:
x = -10 +/- sqrt(96)
if you use the quadratic formula instead, you would wind up with the same answer.
example:
standard form of your equation is:
x^2 + 20x + 4 = 0
a = 1
b = 20
c = 4
quadratic formula is:
x = (-b +/- sqrt(b^2-4ac))/2a
plugging in the values, you get:
x = (-20 +/- sqrt(400-4*1*4))/2 which becomes:
x = (-20 +/- sqrt(384))/2 which becomes:
x = (-20 +/- sqrt(4*96))/2 which becomes:
x = (-20 +/- 2*sqrt(96))/2 which becomes:
x = -10 +/- sqrt(96).
you get the same answer either way as you should.
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