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

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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)   (Show Source): You can put this solution on YOUR website!

Start with the given equation


Factor out the GCF 5d.


Now set each factor equal to zero:
or

or Solve for d in each case


So our answers are

or


--------------------------------------

2)

Start with the given equation.


Subtract 16 from both sides.


Notice that the quadratic is in the form of where , , and


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


Start with the quadratic formula


Plug in , , and


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


Break up the fraction.


Reduce.


or Break up the expression.


So the solutions are or


-------------------------------------------------------------
3)



Start with the given equation.


Add 2 to both sides.


Notice that the quadratic is in the form of where , , and


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


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Subtract from to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the solutions are or


Answer by richwmiller(17219)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=0.111111111111121 is greater than zero. That means that there are two solutions: .




Quadratic expression 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
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