SOLUTION: for the equation x^2+6x=-3 A.find a,b,c.(it will help you mput the equation in standard form first) b.solve the equation using the quadratic formula.

Algebra ->  Square-cubic-other-roots -> SOLUTION: for the equation x^2+6x=-3 A.find a,b,c.(it will help you mput the equation in standard form first) b.solve the equation using the quadratic formula.      Log On


   

Question 396732: for the equation x^2+6x=-3
A.find a,b,c.(it will help you mput the equation in standard form first)
b.solve the equation using the quadratic formula.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Standard form for an equation like this is:
ax%5E2+%2B+bx+%2B+c+=+0
Note the zero on one side. So we start by getting one side of
x%5E2%2B6x=3
to be a zero. The easiest thing is to add -3 to each side:
x%5E2+%2B+6x+%2B+%28-3%29+=+0
We can now "read" the values for a, b and c:
a = 1
b = 6
c = -3

Solving the equation with the Quadratic Formula we get:
x+=+-%286%29+%2B-+sqrt%28%286%29%5E2+-+4%281%29%28-3%29%29%29%2F2%281%29
which simplifies as follows:
x+=+%28-%286%29+%2B-+sqrt%2836+-+4%281%29%28-3%29%29%29%2F2%281%29
x+=+%28-%286%29+%2B-+sqrt%2836+%2B+12%29%29%2F2%281%29
x+=+%28-%286%29+%2B-+sqrt%2848%29%29%2F2%281%29
x+=+%28-6+%2B-+sqrt%2848%29%29%2F2
x+=+%28-6+%2B-+sqrt%2816%2A3%29%29%2F2
x+=+%28-6+%2B-+sqrt%2816%29%2Asqrt%283%29%29%2F2
x+=+%28-6+%2B-+4%2Asqrt%283%29%29%2F2
x+=+%282%28-3+%2B-+2%2Asqrt%283%29%29%29%2F2
x+=+%28cross%282%29%28-3+%2B-+2%2Asqrt%283%29%29%29%2Fcross%282%29
x+=+-3+%2B-+2%2Asqrt%283%29
In long form this is:
x+=+-3+%2B+2%2Asqrt%283%29 or x+=+-3+-+2%2Asqrt%283%29
These are the simplified, exact expressions for the solutions to your equation.