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

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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) About Me  (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:
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3x^2 + 5x - 3 -x = 0
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Combine the 5x and -x to get +4x. This reduces the equation to:
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3x^2 + 4x - 3 = 0
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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:
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x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
.
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:
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x+=+%28-%284%29%2B-sqrt%284%5E2+-+4%2A3%2A%28-3%29%29%29%2F%282%2A3%29
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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:
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x+=+%28-4%2B-sqrt%2816+%2B36%29%29%2F%286%29
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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:
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x+=+%28-4%2B-sqrt%284%2A13%29%29%2F%286%29
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But sqrt%284%2A13%29+=+sqrt%284%29%2Asqrt%2813%29+=+2%2Asqrt%2813%29
.
Substituting this for sqrt(4*13) further simplifies the problem to:
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x+=+%28-4%2B-2%2Asqrt%2813%29%29%2F%286%29
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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:
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x+=+%28-2%2B-sqrt%2813%29%29%2F%283%29
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Now you can write the two answers for x. First use the plus sign between the terms in the
numerator to get:
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x+=+%28-2%2Bsqrt%2813%29%29%2F%283%29
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then use the minus sign to get the other answer for x:
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x+=+%28-2-sqrt%2813%29%29%2F%283%29
.
And there you have the two answers for x
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Hope this helps you understand the problem.
.