SOLUTION: i have worked this problem several times and I havent been able to come close to solving it. 8x^2=30x+8 the ^2 means to the 2nd power. I wasn't sure how to enter exponents. C

Question 107217: i have worked this problem several times and I havent been able to come close to solving it.
8x^2=30x+8 the ^2 means to the 2nd power. I wasn't sure how to enter exponents. Can anyone help me?
Thank you,
Found 2 solutions by Earlsdon, bucky:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
You could try this:
Subtract 30x from both sides.
Now subtract 8 from both sides.
Factor a 2 from this trinomial.
Applying the zero products principle, you get:
Factor this quadratic equation.
Again, apply the zero products principle.
or
If then , so
If then
Solution:

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
To solve for x you can begin by changing the arrangement of the given equation. You want to
have all the terms on the left side of the equation and have the right side equal to zero.
This is a "standard" arrangement for a quadratic equation. Therefore you can get rid of the
two terms on the right side as follows. First subtract 30x from both sides of this equation.
On the right side subtracting 30x cancels out the 30x. And the subtraction of 30x from the left
side makes the equation become:
.

.
Next, following the same type of process, get rid of the 8 on the right side by subtracting
8 from both sides. When you do that the equation is converted to the standard quadratic form:
.

.
Notice that you can simplify this a little bit by dividing both sides (all terms) by 2
because 2 is a factor common to all the numbers of this equation. This division leads the
equation to become:
.

.
Now you can apply the quadratic formula. The quadratic formula says that if you have a quadratic
equation in the standard form of:
.

.
then the solutions for x are given by the equation:
.

.
Well, your equation is certainly in the standard form. Compare like terms of the standard
form with your equation and you will see that:
.
will be the same if a = 4
will be the same if b = -15 and
identifies c
.
So you now know the values for a, b, and c. To solve for x you just substitute these values
into the equation for x above. Substituting these values results in:
.

.
Note that -(-15) is +15. Also note that is +225. And -4*4*-4 is +64. And
finally in the denominator, 2*4 = 8. Substitute these values into the equation for x and
you get:
.

.
The square root of 289 is 17, and when this is substituted the equation for x becomes:
.

.
First use the plus sign in the numerator and you get:
.

.
Then use the minus sign in the numerator"
.

.
So the two answers to this problem are x = 4 and x = -1/4
.
You can validate these answers by substituting them for x in the original problem and
showing that both sides of that equation remain equal.
.
As an example, the original problem is:
.

.
If you set x equal to 4 this equation becomes:
.

.
The and
.
Substituting these results in:
.

.
On the left side the 8*16 = 128 and on the right side the 120 + 8 = 128. So the equation
is 128 = 128 which shows that the equation is true when x = 4. Therefore, x = 4 is a
good answer.
.
You can do the same sort of check by letting x = -1/4 in the original equation and again
showing that the left side of the equation equals the right side of the equation.
.
Hope this helps you to understand the problem and how you can get the two answers for x.
.
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