SOLUTION: Here are three questions I need help with: 1.) 5d^2 - 10d = 0 (factoring problem) 2.) 8x^2 = 16 (factoring problem) 3.) 3m^2 - 5m = -2 (factoring pr

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Here are three questions I need help with: 1.) 5d^2 - 10d = 0 (factoring problem) 2.) 8x^2 = 16 (factoring problem) 3.) 3m^2 - 5m = -2 (factoring pr      Log On


   

Question 248346: Here are three questions I need help with:
1.) 5d^2 - 10d = 0 (factoring problem)
2.) 8x^2 = 16 (factoring problem)
3.) 3m^2 - 5m = -2 (factoring problem)
And my teacher only likes the answers in fractions or radicals, no decimals.
Thank you!
Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

5d%5E2-10d=0 Start with the given equation


5d%28d-2%29=0 Factor out the GCF 5d.


Now set each factor equal to zero:
5d=0 or d-2=0

d=0 or d=2 Solve for d in each case


So our answers are

d=0 or d=2


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2)

8x%5E2+=+16 Start with the given equation.


8x%5E2+-+16=0 Subtract 16 from both sides.


Notice that the quadratic 8x%5E2-16 is in the form of Ax%5E2%2BBx%2BC where A=8, B=0, and C=-16


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-%280%29+%2B-+sqrt%28+%280%29%5E2-4%288%29%28-16%29+%29%29%2F%282%288%29%29 Plug in A=8, B=0, and C=-16


x+=+%28-0+%2B-+sqrt%28+0-4%288%29%28-16%29+%29%29%2F%282%288%29%29 Square 0 to get 0.


x+=+%28-0+%2B-+sqrt%28+0--512+%29%29%2F%282%288%29%29 Multiply 4%288%29%28-16%29 to get -512


x+=+%28-0+%2B-+sqrt%28+0%2B512+%29%29%2F%282%288%29%29 Rewrite sqrt%280--512%29 as sqrt%280%2B512%29


x+=+%28-0+%2B-+sqrt%28+512+%29%29%2F%282%288%29%29 Add 0 to 512 to get 512


x+=+%28-0+%2B-+sqrt%28+512+%29%29%2F%2816%29 Multiply 2 and 8 to get 16.


x+=+%28-0+%2B-+16%2Asqrt%282%29%29%2F%2816%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-0%29%2F%2816%29+%2B-+%2816%2Asqrt%282%29%29%2F%2816%29 Break up the fraction.


x+=+0+%2B-+sqrt%282%29 Reduce.


x+=+sqrt%282%29 or x+=+-sqrt%282%29 Break up the expression.


So the solutions are x+=+sqrt%282%29 or x+=+-sqrt%282%29


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3)



3m%5E2-5m=-2 Start with the given equation.


3m%5E2-5m%2B2=0 Add 2 to both sides.


Notice that the quadratic 3m%5E2-5m%2B2 is in the form of Am%5E2%2BBm%2BC where A=3, B=-5, and C=2


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-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%283%29%282%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-5, and C=2


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


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


m+=+%285+%2B-+sqrt%28+25-24+%29%29%2F%282%283%29%29 Multiply 4%283%29%282%29 to get 24


m+=+%285+%2B-+sqrt%28+1+%29%29%2F%282%283%29%29 Subtract 24 from 25 to get 1


m+=+%285+%2B-+sqrt%28+1+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


m+=+%285+%2B-+1%29%2F%286%29 Take the square root of 1 to get 1.


m+=+%285+%2B+1%29%2F%286%29 or m+=+%285+-+1%29%2F%286%29 Break up the expression.


m+=+%286%29%2F%286%29 or m+=++%284%29%2F%286%29 Combine like terms.


m+=+1 or m+=+2%2F3 Simplify.


So the solutions are m+=+1 or m+=+2%2F3


Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
1.) 5d^2 - 10d = 0 (factoring problem)
5d(d-2)=0
d=0 and d=2
2.) 8x^2 = 16 (factoring problem)
8(x^2)=8*2
divide by 2
x^2=2
x=+\-sqrt2
3.) 3m^2 - 5m = -2 (factoring problem)
divide by 3
m^2-5/3m=-2/3
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1.66666666666667x%2B0.666666666666667+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1.66666666666667%29%5E2-4%2A1%2A0.666666666666667=0.111111111111121.

Discriminant d=0.111111111111121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1.66666666666667%2B-sqrt%28+0.111111111111121+%29%29%2F2%5Ca.




Quadratic expression 1x%5E2%2B-1.66666666666667x%2B0.666666666666667 can be factored:

Again, the answer is: 1.00000000000001, 0.666666666666661. Here's your graph:

complete the square
add 25/36 to both sides
m^2-5/3m+25/36=-24/36+25/36=1 /36
factor
(m-5/6)^2=(1/6)^2
m-5/6=+\- 1/6
add 5/6 to both sides
m=4/6=2/3
m=6/6=1