SOLUTION: 1. 5/2x^2-3/2x-1/4=0 2. 12m^2-192=0 if you could write out how to do it it would help me so much thanks

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 1. 5/2x^2-3/2x-1/4=0 2. 12m^2-192=0 if you could write out how to do it it would help me so much thanks      Log On


   

Question 395382: 1. 5/2x^2-3/2x-1/4=0
2. 12m^2-192=0
if you could write out how to do it it would help me so much thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

%285%2F2%29x%5E2-%283%2F2%29x-1%2F4=0 Start with the given equation.


10x%5E2-6x-1=0 Multiply EVERY term by the LCD 4 to clear out the fractions.


Notice that the quadratic 10x%5E2-6x-1 is in the form of Ax%5E2%2BBx%2BC where A=10, B=-6, and C=-1


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2810%29%28-1%29+%29%29%2F%282%2810%29%29 Plug in A=10, B=-6, and C=-1


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2810%29%28-1%29+%29%29%2F%282%2810%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%2810%29%28-1%29+%29%29%2F%282%2810%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36--40+%29%29%2F%282%2810%29%29 Multiply 4%2810%29%28-1%29 to get -40


x+=+%286+%2B-+sqrt%28+36%2B40+%29%29%2F%282%2810%29%29 Rewrite sqrt%2836--40%29 as sqrt%2836%2B40%29


x+=+%286+%2B-+sqrt%28+76+%29%29%2F%282%2810%29%29 Add 36 to 40 to get 76


x+=+%286+%2B-+sqrt%28+76+%29%29%2F%2820%29 Multiply 2 and 10 to get 20.


x+=+%286+%2B-+2%2Asqrt%2819%29%29%2F%2820%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%286%2B2%2Asqrt%2819%29%29%2F%2820%29 or x+=+%286-2%2Asqrt%2819%29%29%2F%2820%29 Break up the expression.


x+=+%283%2Bsqrt%2819%29%29%2F%2810%29 or x+=+%283-sqrt%2819%29%29%2F%2810%29 Reduce.


So the solutions are x+=+%283%2Bsqrt%2819%29%29%2F%2810%29 or x+=+%283-sqrt%2819%29%29%2F%2810%29


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# 2



12m%5E2-192=0 Start with the given equation.


Notice that the quadratic 12m%5E2-192 is in the form of Am%5E2%2BBm%2BC where A=12, B=0, and C=-192


Let's use the quadratic formula to solve for "m":


m+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


m+=+%28%280%29+%2B-+sqrt%28+%280%29%5E2-4%2812%29%28-192%29+%29%29%2F%282%2812%29%29 Plug in A=12, B=0, and C=-192


m+=+%280+%2B-+sqrt%28+0-4%2812%29%28-192%29+%29%29%2F%282%2812%29%29 Square 0 to get 0.


m+=+%280+%2B-+sqrt%28+0--9216+%29%29%2F%282%2812%29%29 Multiply 4%2812%29%28-192%29 to get -9216


m+=+%280+%2B-+sqrt%28+0%2B9216+%29%29%2F%282%2812%29%29 Rewrite sqrt%280--9216%29 as sqrt%280%2B9216%29


m+=+%280+%2B-+sqrt%28+9216+%29%29%2F%282%2812%29%29 Add 0 to 9216 to get 9216


m+=+%280+%2B-+sqrt%28+9216+%29%29%2F%2824%29 Multiply 2 and 12 to get 24.


m+=+%280+%2B-+96%29%2F%2824%29 Take the square root of 9216 to get 96.


m+=+%280+%2B+96%29%2F%2824%29 or m+=+%280+-+96%29%2F%2824%29 Break up the expression.


m+=+%2896%29%2F%2824%29 or m+=++%28-96%29%2F%2824%29 Combine like terms.


m+=+4 or m+=+-4 Simplify.


So the solutions are m+=+4 or m+=+-4


If you need more help, email me at jim_thompson5910@hotmail.com

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Jim