SOLUTION: Solve using the quadratic formula: 5x^2 + x = 3 I have four choices: a) -1 plus minus sqrt16 ----------- ------ 5 b) -1 plus minus sqrt61 ----------- -

Algebra ->  Equations -> SOLUTION: Solve using the quadratic formula: 5x^2 + x = 3 I have four choices: a) -1 plus minus sqrt16 ----------- ------ 5 b) -1 plus minus sqrt61 ----------- -      Log On


   

Question 69880: Solve using the quadratic formula:
5x^2 + x = 3
I have four choices:
a) -1 plus minus sqrt16
------------------
5
b) -1 plus minus sqrt61
--------------------
5
c) -1 plus minus sqrt 16
---------------------
10
d) -1 plus minus sqrt 61
-------------------
10
Can anyone help me get the concept of the quadratic formula? Thank you very much!
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2+%2B+x+=+3
The quadratic formula says that if you are given an equation in the form:
ax%5E2+%2B+bx+%2B+c+=+0
then the values of x that satisfy this equation are given by the two equations:
x+=+%28-b%2F%282%2Aa%29%29+%2B+sqrt%28b%5E2+-+4%2Aa%2Ac%29%2F%282%2Aa%29 and
x+=+%28-b%2F%282%2Aa%29%29+-+sqrt%28b%5E2+-+4%2Aa%2Ac%29%2F%282%2Aa%29
So the first thing we need to do is to get the problem you are given into the form of the
quadratic formula. Note that the quadratic formula has a zero on the right side. However,
your equation has a 3 on the right. So you need to subtract 3 from the right side of
your equation, but if you do you must also subtract 3 from the left side.
When you do the subtraction of 3 from both sides, the left and right sides become:
5x%5E2+%2B+x+-+3+=+0
That's more like it. You can now compare the left side of this equation with the left
side of the quadratic formula. Note that "a" in the quadratic formula is the multiplier
of the x%5E2 term. The multiplier of x%5E2 in your equation is 5. Therefore,
you can deduce that a+=+5. Similarly, b in the quadratic formula is the multiplier
of the x term. The multiplier of the x term in your equation is +1. This time you can
deduce that b+=+1. Finally c in the quadratic formula is the constant term on the left,
side. In your problem the constant term is -3. Therefore, c = -3.
Now you have all the information you need to find the values for x that make the equation
true. All that you have to do is to plug in the appropriate values for a, b, and c.
The first value of x is determined from the equation:
x+=+%28-b%2F%282%2Aa%29%29+%2B+sqrt%28b%5E2+-+4%2Aa%2Ac%29%2F%282%2Aa%29
After the substitutions this equation becomes:
x+=+%28-%281%29%2F%282%2A5%29%29+%2B+sqrt%28%281%29%5E2+-+4%2A5%2A%28-3%29%29%2F%282%2A5%29
This simplifies to:
x+=+%28-1%2F10%29+%2B+sqrt%281+-+%28-60%29%29%2F10
which further simplifies to:
x+=+%28-1%2F10%29+%2B+sqrt%2861%29%2F10
By comparing this answer for x with the second value of x you can notice that the only
difference is the sign between the first term and the square root term. In the first
answer the sign is + and we calculated that. The calculations for the second answer is:
x+=+%28-1%2F10%29+-+sqrt%2861%29%2F10
which has the minus sign between the terms.
With a little thought you will be able to see that the answer is the same as answer D.
[The denominator 10 in our answers is common to both terms so that both numerators
can be combined over this common denominator.]
Hope this helps you understand the quadratic formula a little better.