SOLUTION: what is the answer step by step to the following quadratic equations ? x squared-4x-15=0 x squared+8x-33=0 x squared+5x+2=0 3xsquared-3x+6=0 Help would be great i need it bad

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: what is the answer step by step to the following quadratic equations ? x squared-4x-15=0 x squared+8x-33=0 x squared+5x+2=0 3xsquared-3x+6=0 Help would be great i need it bad      Log On


   

Question 120709: what is the answer step by step to the following quadratic equations ?
x squared-4x-15=0
x squared+8x-33=0
x squared+5x+2=0
3xsquared-3x+6=0
Help would be great i need it bad
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
what is the answer step by step to the following quadratic equations ?
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These need to be solved using the quadratic formula, which is:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
x^2 - 4x - 15 = 0
In this problem a = 1; b =-4; c =-15; substitute these value in the quad formula
x+=+%28-%28-4%29+%2B-+sqrt%28-4%5E2+-+4+%2A+1+%2A+-15+%29%29%2F%282%2A1%29+
x+=+%284+%2B-+sqrt%2816+-+%28-60%29+%29%29%2F%282%29+
x+=+%284+%2B-+sqrt%2816+%2B+60+%29%29%2F%282%29+; remember minus a minus is a plus
x+=+%284+%2B-+sqrt%2876%29%29%2F%282%29+
x+=+%284+%2B-+8.7178%29%2F2+; find the square root of 76 with a calc
Two solutions
Solution 1:
x+=+%284+%2B+8.7178%29%2F2+
x+=+12.7178%2F2
x = 6.3589 is solution 1
Solution 2:
x+=+%284+-+8.7178%29%2F2+
x+=+-4.7178%2F2
x = -2.3589 is solution 2
:
:
x^2 + 8x - 33 = 0
In this problem a = 1; b = 8; c =-33, substitute these in the quad formula
x+=+%28-8+%2B-+sqrt%288%5E2-+4+%2A+1+%2A+-33+%29%29%2F%282%2A1%29+
x+=+%28-8+%2B-+sqrt%2864+-+%28-132%29+%29%29%2F%282%29+
x+=+%28-8+%2B-+sqrt%2864+%2B+132+%29%29%2F%282%29+
x+=+%28-8+%2B-+sqrt%28196+%29%29%2F%282%29+
x+=+%28-8+%2B-+14%29%2F2+
Solution 1
x+=+%28-8+%2B+14%29%2F2+
x+=+%28%2B6%29%2F2+
x = 3 is solution 1
Solution 2
x+=+%28-8+-+14%29%2F2
x+=+%28-22%29%2F2
x = -11 is solution 2
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Note that these solutions are both integers, so we could have just factored
(x+11)(x-3)= 0 would have saved a lot of time
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:
x^2 + 5x + 2 = 0
You should be getting the hang of it now
x+=+%28-5+%2B-+sqrt%285%5E2+-+4+%2A+1+%2A+2+%29%29%2F%282%2A1%29+
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Do the math on this one just like we did on the 1st two
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You should get: x = -4.56 and x = -.438, (neither comes out even)
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This one is a special case, does not have any real roots
we shall see why as we proceed with the quad formula
3x^2 - 3x + 6 = 0
x+=+%28-%28-3%29+%2B-+sqrt%28-3%5E2-+4+%2A+3+%2A+6+%29%29%2F%282%2A3%29+
x+=+%283+%2B-+sqrt%289+-+72+%29%29%2F%286%29+
x+=+%283+%2B-+sqrt%28-63+%29%29%2F%286%29+
we have a square root of a negative number so there is no real roots
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Look up the word "discriminant" in the index of your algebra book.
This is related to what we just did.
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Did this make sense to you. It's very important that you understand exactly what's going on here. Do you have any questions?