SOLUTION: can you show me the steps of solving the quadratic equation but in the other form that's -(b)+-square root of b squared minus 4ac over 2a because i know how to solve it but i don't

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: can you show me the steps of solving the quadratic equation but in the other form that's -(b)+-square root of b squared minus 4ac over 2a because i know how to solve it but i don't      Log On


   



Question 415558: can you show me the steps of solving the quadratic equation but in the other form that's -(b)+-square root of b squared minus 4ac over 2a because i know how to solve it but i don't understand it.
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
eg: x%5E2+-+5x+%2B+7+=+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-5x%2B7+=+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=%28-5%29%5E2-4%2A1%2A7=-3.

The discriminant -3 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -3 is + or - sqrt%28+3%29+=+1.73205080756888.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B7+%29

example 2:
x%5E2+-+x+-12+=+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-1x%2B-12+=+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=%28-1%29%5E2-4%2A1%2A-12=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+49+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%28-1%29-sqrt%28+49+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B-1x%2B-12 can be factored:
1x%5E2%2B-1x%2B-12+=+%28x-4%29%2A%28x--3%29
Again, the answer is: 4, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-12+%29


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The equation has to be in the form y+=+ax%5E2+%2B+bx+%2B+c
There are 2 roots. You can have:
(1) 2 real roots
(2) 1 real root
(3) 2 imaginary roots
(4) no roots
All this information can be gotten out of the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
notice the +- before the square root sign
You could express the formula as
x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
and
x%5B2%5D+=+%28-b+-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
These are the x-coordinates of the 2 roots of the equation
example:
2x%5E2+%2B+5x+%2B+3+=+0
The factors will look like +%28x+-+x%5B1%5D%29%2A%28x+-+x%5B2%5D%29+
a+=+2
b+=+5
c+=+3
x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x%5B1%5D+=+%28-5+%2B+sqrt%28+5%5E2-4%2A2%2A3+%29%29%2F%282%2A2%29+
x%5B1%5D+=+%28-5+%2B+sqrt%28+25+-+24+%29%29%2F4+
x%5B1%5D+=+%28-5+%2B+1+%29%2F4+
x%5B1%5D+=+-1
and the other root is
x%5B2%5D+=+%28-5+-+sqrt%28+25+-+4%2A2%2A3+%29%29%2F%282%2A2%29+
x%5B2%5D+=+%28-5+-+sqrt%28+25+-+24+%29%29%2F4+
x%5B2%5D+=+%28-5+-+1%29%2F4+
x%5B2%5D+=+-3%2F2
Now I can rewrite what I found as:
x+-+x%5B1%5D+=+0
x+-+x%5B2%5D+=+0
and
x+%2B+1+=+0
x+%2B+%283%2F2%29+=+0
So, the factors of the equation are:
+%28x+%2B+1%29%2A%28x+%2B+3%2F2%29+=+0
x%5E2+%2B+x+%2B+%283%2F2%29%2Ax+%2B+3%2F2+=+0
x%5E2+%2B+%285%2F2%29%2Ax+%2B+3%2F2+=+0
Multiply both sides by 2
2x%5E2+%2B+5x+%2B+3+=+0
which is the equation, so the roots are -1 and -3/2
Here is the plot:
+graph%28+400%2C+400%2C+-4%2C+4%2C+-2%2C+8%2C+2x%5E2+%2B+5x+%2B+3%29+