Solve for y square root of 10y^2-4y-5=3y

Math
10y2-4y-5=3y
To remove the radical on the left side of the equation, square both sides of the equation.
10y2-4y-52=(3y)2
Simplify each side of the equation.
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Multiply the exponents in ((10y2-4y-5)12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(10y2-4y-5)12⋅2=(3y)2
Cancel the common factor of 2.
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Cancel the common factor.
(10y2-4y-5)12⋅2=(3y)2
Rewrite the expression.
(10y2-4y-5)1=(3y)2
(10y2-4y-5)1=(3y)2
(10y2-4y-5)1=(3y)2
Simplify.
10y2-4y-5=(3y)2
Apply the product rule to 3y.
10y2-4y-5=32y2
Raise 3 to the power of 2.
10y2-4y-5=9y2
10y2-4y-5=9y2
Solve for y.
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Move all terms containing y to the left side of the equation.
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Subtract 9y2 from both sides of the equation.
10y2-4y-5-9y2=0
Subtract 9y2 from 10y2.
y2-4y-5=0
y2-4y-5=0
Factor y2-4y-5 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -5 and whose sum is -4.
-5,1
Write the factored form using these integers.
(y-5)(y+1)=0
(y-5)(y+1)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
y-5=0
y+1=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
y-5=0
Add 5 to both sides of the equation.
y=5
y=5
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
y+1=0
Subtract 1 from both sides of the equation.
y=-1
y=-1
The final solution is all the values that make (y-5)(y+1)=0 true.
y=5,-1
y=5,-1
Exclude the solutions that do not make 10y2-4y-5=3y true.
y=5
Solve for y square root of 10y^2-4y-5=3y

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