# Solve for y square root of 11y+3-2y=0 11y+3-2y=0
Add 2y to both sides of the equation.
11y+3=2y
To remove the radical on the left side of the equation, square both sides of the equation.
11y+32=(2y)2
Simplify each side of the equation.
Multiply the exponents in ((11y+3)12)2.
Apply the power rule and multiply exponents, (am)n=amn.
(11y+3)12⋅2=(2y)2
Cancel the common factor of 2.
Cancel the common factor.
(11y+3)12⋅2=(2y)2
Rewrite the expression.
(11y+3)1=(2y)2
(11y+3)1=(2y)2
(11y+3)1=(2y)2
Simplify.
11y+3=(2y)2
Apply the product rule to 2y.
11y+3=22y2
Raise 2 to the power of 2.
11y+3=4y2
11y+3=4y2
Solve for y.
Subtract 4y2 from both sides of the equation.
11y+3-4y2=0
Factor the left side of the equation.
Factor -1 out of 11y+3-4y2.
Reorder the expression.
Move 3.
11y-4y2+3=0
Reorder 11y and -4y2.
-4y2+11y+3=0
-4y2+11y+3=0
Factor -1 out of -4y2.
-(4y2)+11y+3=0
Factor -1 out of 11y.
-(4y2)-(-11y)+3=0
Rewrite 3 as -1(-3).
-(4y2)-(-11y)-1⋅-3=0
Factor -1 out of -(4y2)-(-11y).
-(4y2-11y)-1⋅-3=0
Factor -1 out of -(4y2-11y)-1(-3).
-(4y2-11y-3)=0
-(4y2-11y-3)=0
Factor.
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=4⋅-3=-12 and whose sum is b=-11.
Factor -11 out of -11y.
-(4y2-11y-3)=0
Rewrite -11 as 1 plus -12
-(4y2+(1-12)y-3)=0
Apply the distributive property.
-(4y2+1y-12y-3)=0
Multiply y by 1.
-(4y2+y-12y-3)=0
-(4y2+y-12y-3)=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
-((4y2+y)-12y-3)=0
Factor out the greatest common factor (GCF) from each group.
-(y(4y+1)-3(4y+1))=0
-(y(4y+1)-3(4y+1))=0
Factor the polynomial by factoring out the greatest common factor, 4y+1.
-((4y+1)(y-3))=0
-((4y+1)(y-3))=0
Remove unnecessary parentheses.
-(4y+1)(y-3)=0
-(4y+1)(y-3)=0
-(4y+1)(y-3)=0
Multiply each term in -(4y+1)(y-3)=0 by -1
Multiply each term in -(4y+1)(y-3)=0 by -1.
(-(4y+1)(y-3))⋅-1=0⋅-1
Simplify (-(4y+1)(y-3))⋅-1.
Simplify by multiplying through.
Apply the distributive property.
(-(4y)-1⋅1)(y-3)⋅-1=0⋅-1
Multiply.
Multiply 4 by -1.
(-4y-1⋅1)(y-3)⋅-1=0⋅-1
Multiply -1 by 1.
(-4y-1)(y-3)⋅-1=0⋅-1
(-4y-1)(y-3)⋅-1=0⋅-1
(-4y-1)(y-3)⋅-1=0⋅-1
Expand (-4y-1)(y-3) using the FOIL Method.
Apply the distributive property.
(-4y(y-3)-1(y-3))⋅-1=0⋅-1
Apply the distributive property.
(-4y⋅y-4y⋅-3-1(y-3))⋅-1=0⋅-1
Apply the distributive property.
(-4y⋅y-4y⋅-3-1y-1⋅-3)⋅-1=0⋅-1
(-4y⋅y-4y⋅-3-1y-1⋅-3)⋅-1=0⋅-1
Simplify and combine like terms.
Simplify each term.
Multiply y by y by adding the exponents.
Move y.
(-4(y⋅y)-4y⋅-3-1y-1⋅-3)⋅-1=0⋅-1
Multiply y by y.
(-4y2-4y⋅-3-1y-1⋅-3)⋅-1=0⋅-1
(-4y2-4y⋅-3-1y-1⋅-3)⋅-1=0⋅-1
Multiply -3 by -4.
(-4y2+12y-1y-1⋅-3)⋅-1=0⋅-1
Rewrite -1y as -y.
(-4y2+12y-y-1⋅-3)⋅-1=0⋅-1
Multiply -1 by -3.
(-4y2+12y-y+3)⋅-1=0⋅-1
(-4y2+12y-y+3)⋅-1=0⋅-1
Subtract y from 12y.
(-4y2+11y+3)⋅-1=0⋅-1
(-4y2+11y+3)⋅-1=0⋅-1
Apply the distributive property.
-4y2⋅-1+11y⋅-1+3⋅-1=0⋅-1
Simplify.
Multiply -1 by -4.
4y2+11y⋅-1+3⋅-1=0⋅-1
Multiply -1 by 11.
4y2-11y+3⋅-1=0⋅-1
Multiply 3 by -1.
4y2-11y-3=0⋅-1
4y2-11y-3=0⋅-1
4y2-11y-3=0⋅-1
Multiply 0 by -1.
4y2-11y-3=0
4y2-11y-3=0
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=4⋅-3=-12 and whose sum is b=-11.
Factor -11 out of -11y.
4y2-11y-3=0
Rewrite -11 as 1 plus -12
4y2+(1-12)y-3=0
Apply the distributive property.
4y2+1y-12y-3=0
Multiply y by 1.
4y2+y-12y-3=0
4y2+y-12y-3=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(4y2+y)-12y-3=0
Factor out the greatest common factor (GCF) from each group.
y(4y+1)-3(4y+1)=0
y(4y+1)-3(4y+1)=0
Factor the polynomial by factoring out the greatest common factor, 4y+1.
(4y+1)(y-3)=0
(4y+1)(y-3)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
4y+1=0
y-3=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
4y+1=0
Subtract 1 from both sides of the equation.
4y=-1
Divide each term by 4 and simplify.
Divide each term in 4y=-1 by 4.
4y4=-14
Cancel the common factor of 4.
Cancel the common factor.
4y4=-14
Divide y by 1.
y=-14
y=-14
Move the negative in front of the fraction.
y=-14
y=-14
y=-14
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
y-3=0
Add 3 to both sides of the equation.
y=3
y=3
The final solution is all the values that make (4y+1)(y-3)=0 true.
y=-14,3
y=-14,3
Exclude the solutions that do not make 11y+3-2y=0 true.
y=3
Solve for y square root of 11y+3-2y=0

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