how do i solve for y?

Question

4y^2 + 4 = 10y

Answer 1

4y^2 + 4 = 10y
Transpose into normal quadratic form:
4y^2 - 10Y + 4 = 0
Factor into binomial:
(4y - 2)(y - 2) = 0
Either factor can be 0:
(4y - 2) = 0, 4y = 2, y = 1/2
Or:
(y - 2) = 0, y = 2

Answer 2

Since there is a y^2 we need to find it quadratically. First you need to bring everything to one side:

4y^2 + 4 =10y
4y^2 - 10y + 4 = 0

Now you can either solve it by factoring or with the quadratic formula:

By factoring:
4y^2 - 10 + 4 = 0
(2y - 1)(2y - 4) = 0
Now let each expression in parentheses equal to 0 and solve for y that way.

By Quadratic formula:

Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a, for ax^2 + bx + c = 0
So we substitute the values:
a = 4
b = -10
c = 4

(-b +/- sqrt(b^2 - 4ac)) / 2a = y
(-(-10) +/- sqrt((-10)^2 - 4(4)(4))) / 2(4) = y
(10 +/- sqrt(100 - 64)) / 8 = y
(10 +/- sqrt(36))/8 = y
(10 +/- 6) / 8 = y
y = 1, 1/2

Answer 3

There are several methods for solvind quadratic equations... the most used one is by the general formula:
Suppose you have an equation of the form ax^2+bx+c=0 then x=(-b+Sqrt(b^2-4ac))/(2a) or x=(-b-Sqrt(b^2-4ac))/(2a)
So, first your equation is equivalent to 4y^2-10y+4=0 so a=4, b=-10 c=4
so y=(10+Sqrt(100-64))/8=(10+Sqrt(36))/8=(10+6)/8=16/8=2
or y=(10-Sqrt(100-64))/8=(10-Sqrt(36))/8=(10-6)/8=4/8=1/2

Answer 4

4y^2 + 4 = 10y
4y^2 - 10y + 4 = 0
2y^2 - 5y + 4 = 0
(y - 2)(2y - 1) = 0
y = 2 or y = 1/2

Answer 5

Standard quadratic, but it needs rearranging first...

4y^2 + 4 = 10y

Divide through by 2:
2y^2 + 2 = 5y

Subtract 5y from both sides:
2y^2 -5y + 2 = 0

Factorise (I'll start it, but let you fill in the blanks...)
(2y - ?)(y - ??) = 0

For this to be true, either the first bracket is zero, or the second bracket is 0. That gives you two possible values of y.

Answer 6

4y^2 - 10y +4 = 0
(2y - 4)(2y - 1)= 0
2y-4=0 or 2y-1=0
2y=4 or 2y=1
y=2 or y=1/2

Answer 7

4y^2+4=10y
2y^2-5y+2=0
2y^2-4y-y+2=0
2y(y-2)-1(y-2)=0
(y-2)(2y-1)=0
y=2,1/2 ANS

Answer 8

move the 10y over to the other side then use the quadratic equation

Answer 9

subtract 10 y from both sides
then use quadratic..
or just factor