SOLUTION: hello :) hope anyone can help me Solve by using the quadratic equation X=- b+_ sqrt ( (B)^2 -4(a) (c) All over 2(a) 1.) a^2+2(a+3)=0 2.) x^2-3(2x+3)=0 3.) 3y(y-5)=6

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: hello :) hope anyone can help me Solve by using the quadratic equation X=- b+_ sqrt ( (B)^2 -4(a) (c) All over 2(a) 1.) a^2+2(a+3)=0 2.) x^2-3(2x+3)=0 3.) 3y(y-5)=6       Log On


   

Question 980897: hello :) hope anyone can help me
Solve by using the quadratic equation
X=- b+_ sqrt ( (B)^2 -4(a) (c)
All over 2(a)
1.) a^2+2(a+3)=0
2.) x^2-3(2x+3)=0
3.) 3y(y-5)=6
4.) 2(3x^2+1) =
Hope anyone can help me solve :)
Kindly could you explain how too?
Thnak you bery much!

Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2.) x^2-3(2x+3)=0
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Put in this format:
x^2-6x - 9 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B-9+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-6%29%5E2-4%2A1%2A-9=72.

Discriminant d=72 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+72+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+72+%29%29%2F2%5C1+=+7.24264068711928
x%5B2%5D+=+%28-%28-6%29-sqrt%28+72+%29%29%2F2%5C1+=+-1.24264068711928

Quadratic expression 1x%5E2%2B-6x%2B-9 can be factored:
1x%5E2%2B-6x%2B-9+=+%28x-7.24264068711928%29%2A%28x--1.24264068711928%29
Again, the answer is: 7.24264068711928, -1.24264068711928. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B-9+%29

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Do the others the same way.
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#4 is not an equation, nothing on the right side.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1.)
a%5E2%2B2%28a%2B3%29=0

a%5E2%2B2a%2B6=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ...note your coefficient a=1, unknown variable x is a, coefficient ba=2, and constant c=6

a+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29+

a+=+%28-2+%2B-+sqrt%28+4-24+%29%29%2F2+

a+=+%28-2+%2B-+sqrt%28+-20+%29%29%2F2+
a+=+%28-2+%2B-+sqrt%28+-4%2A5+%29%29%2F2+
a+=+%28-2+%2B-+2sqrt%28+5+%29%2Ai%29%2F2+
a+=+%28-cross%282%291+%2B-+cross%282%29sqrt%28+5+%29%2Ai%29%2Fcross%282%29+
a+=+%28-1+%2B-sqrt%28+5+%29%2Ai%29+
solutions: there is no real solutions (so, there is no x-intercepts), just complex solutions

a+=+-1+%2Bsqrt%28+5+%29%2Ai+
or
a+=+-1+-sqrt%28+5+%29%2Ai+





2.)
x%5E2-3%282x%2B3%29=0
x%5E2-6x-9=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A%28-9%29+%29%29%2F%282%2A1%29+
x+=+%286+%2B-+sqrt%28+36%2B36+%29%29%2F2+
x+=+%286+%2B-+sqrt%28+2%2A36+%29%29%2F2+
x+=+%286+%2B-+sqrt%28+2%2A6%5E2+%29%29%2F2+
x+=+%286+%2B-+6sqrt%28+2+%29%29%2F2+
x+=+%28cross%286%293+%2B-+cross%286%293sqrt%28+2+%29%29%2Fcross%282%291+
x+=+%283+%2B-+3sqrt%28+2+%29%29+
solutions:
exact
x+=+3+%2B+3sqrt%28+2+%29+
or
x+=+3+-3sqrt%28+2+%29+

approximate:
x+=+7.24+
or
x+=+-1.24+

3.)
3y%28y-5%29=6
3y%5E2-15y=6
3y%5E2-15y-6=0
y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y+=+%28-%28-15%29+%2B-+sqrt%28+%28-15%29%5E2-4%2A3%2A%28-6%29+%29%29%2F%282%2A3%29+
y+=+%2815+%2B-+sqrt%28+225%2B72+%29%29%2F6+
y+=+%2815+%2B-+sqrt%28+297+%29%29%2F6+
y+=+%2815+%2B-+17.23%29%2F6+
solutions:

y+=+%2815+%2B+17.23%29%2F6+
y+=+32.23%2F6+
y+=+5.37+
or
y+=+%2815+-+17.23%29%2F6+
y+=+-2.23%2F6+
y+=+-0.37+

4.)
2%283x%5E2%2B1%29+=0
6x%5E2%2B2+=0
6x%5E2+=-2
x%5E2+=-2%2F6
x%5E2+=-1%2F3
x+=sqrt%28-1%2F3%29
solutions: complex
x+=++sqrt%28-1%2F3%29+=>x+=+sqrt%28-1%29%2Fsqrt%283%29=>x+=+i%2Fsqrt%283%29

or
x+=+-+sqrt%28-1%2F3%29+=>x+=+-sqrt%28-1%29%2Fsqrt%283%29=>x+=+-i%2Fsqrt%283%29