SOLUTION: Please help me solve a few of my homework problems from my CNM professor; 1. 3x^2-5x-12=0 2. x^2+x=2 3. x^2-12=x 4. x^2-6x+1 5. 2x^2-11x-21=0 Thank you greatly

Algebra ->  Algebra  -> Radicals -> SOLUTION: Please help me solve a few of my homework problems from my CNM professor; 1. 3x^2-5x-12=0 2. x^2+x=2 3. x^2-12=x 4. x^2-6x+1 5. 2x^2-11x-21=0 Thank you greatly      Log On

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Question 191876: Please help me solve a few of my homework problems from my CNM professor;
1. 3x^2-5x-12=0
2. x^2+x=2
3. x^2-12=x
4. x^2-6x+1
5. 2x^2-11x-21=0
Thank you greatly for any help. It is appreciated:)
Answer by jim_thompson5910(28536) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first three to get you going...


# 1



3x%5E2-5x-12=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=3, b=-5, and c=-12


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-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%283%29%28-12%29+%29%29%2F%282%283%29%29 Plug in a=3, b=-5, and c=-12


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%283%29%28-12%29+%29%29%2F%282%283%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%283%29%28-12%29+%29%29%2F%282%283%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25--144+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-12%29 to get -144


x+=+%285+%2B-+sqrt%28+25%2B144+%29%29%2F%282%283%29%29 Rewrite sqrt%2825--144%29 as sqrt%2825%2B144%29


x+=+%285+%2B-+sqrt%28+169+%29%29%2F%282%283%29%29 Add 25 to 144 to get 169


x+=+%285+%2B-+sqrt%28+169+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%285+%2B-+13%29%2F%286%29 Take the square root of 169 to get 13.


x+=+%285+%2B+13%29%2F%286%29 or x+=+%285+-+13%29%2F%286%29 Break up the expression.


x+=+%2818%29%2F%286%29 or x+=++%28-8%29%2F%286%29 Combine like terms.


x+=+3 or x+=+-4%2F3 Simplify.


So the answers are x+=+3 or x+=+-4%2F3





# 2




x%5E2%2Bx=2 Start with the given equation.


x%5E2%2Bx-2=0 Subtract 2 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=1, and c=-2


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-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%28-2%29+%29%29%2F%282%281%29%29 Plug in a=1, b=1, and c=-2


x+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-2%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--8+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-2%29 to get -8


x+=+%28-1+%2B-+sqrt%28+1%2B8+%29%29%2F%282%281%29%29 Rewrite sqrt%281--8%29 as sqrt%281%2B8%29


x+=+%28-1+%2B-+sqrt%28+9+%29%29%2F%282%281%29%29 Add 1 to 8 to get 9


x+=+%28-1+%2B-+sqrt%28+9+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-1+%2B-+3%29%2F%282%29 Take the square root of 9 to get 3.


x+=+%28-1+%2B+3%29%2F%282%29 or x+=+%28-1+-+3%29%2F%282%29 Break up the expression.


x+=+%282%29%2F%282%29 or x+=++%28-4%29%2F%282%29 Combine like terms.


x+=+1 or x+=+-2 Simplify.


So the answers are x+=+1 or x+=+-2



# 3

x%5E2-12=x Start with the given equation.


x%5E2-12-x=0 Subtract "x" from both sides.


x%5E2-x-12=0 Rearrange the terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-1, and c=-12


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-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-1, and c=-12


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--48+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-12%29 to get -48


x+=+%281+%2B-+sqrt%28+1%2B48+%29%29%2F%282%281%29%29 Rewrite sqrt%281--48%29 as sqrt%281%2B48%29


x+=+%281+%2B-+sqrt%28+49+%29%29%2F%282%281%29%29 Add 1 to 48 to get 49


x+=+%281+%2B-+sqrt%28+49+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+7%29%2F%282%29 Take the square root of 49 to get 7.


x+=+%281+%2B+7%29%2F%282%29 or x+=+%281+-+7%29%2F%282%29 Break up the expression.


x+=+%288%29%2F%282%29 or x+=++%28-6%29%2F%282%29 Combine like terms.


x+=+4 or x+=+-3 Simplify.


So the answers are x+=+4 or x+=+-3