SOLUTION: I believe I have this correct. Can you please check it for me. 3x^2+5x-3=x 3x^2+5x-3-x=0 3x^2+4x=3 Thank You

Question 107339: I believe I have this correct. Can you please check it for me.
3x^2+5x-3=x
3x^2+5x-3-x=0
3x^2+4x=3
Thank You
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.
3x^2+5x-3=x <=== OK
3x^2+5x-3-x=0 <=== OK
3x^2+4x=3 <=== OK, but why not solve for x by using the quadratic formula
.
Start with your second equation:
.
3x^2 + 5x - 3 -x = 0
.
Combine the 5x and -x to get +4x. This reduces the equation to:
.
3x^2 + 4x - 3 = 0
.
Now recognize that this is in the standard quadratic form of ax^2 + bx + c = 0 in which (by
comparing your equation with the standard quadratic form) a = 3, b = 4, and c = -3.
.
The quadratic formula says that when you have a quadratic equation in the standard quadratic
form, the answer for x is given by:
.

.
So to get the answer for x all you have to do is appropriately substitute 3 for a, 4 for b,
and -3 for c in the answer equation. When you do that you get:
.

.
notice that -(4) is just -4. Then within the radical sign 4^2 is 16 and -4*3*(-3) is +36.
And finally in the denominator 2*3 = 6. Substitute these values into the equation and you get:
.

.
The terms under the radical sign add up to 52. And this 52 factors to 4*13. Substituting this
into the answer for x results in:
.

.
But
.
Substituting this for sqrt(4*13) further simplifies the problem to:
.

.
Notice that both terms in the numerator have 2 as a factor. And the denominator also has
2 as a factor. So, if you divide the numerator by 2 and the denominator by 2, the equation
for x reduces to:
.

.
Now you can write the two answers for x. First use the plus sign between the terms in the
numerator to get:
.

.
then use the minus sign to get the other answer for x:
.

.
And there you have the two answers for x
.
Hope this helps you understand the problem.
.

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