# Solve for y 0.9=v(50-y^2)

0.9=v(50-y2)
Rewrite the equation as v(50-y2)=0.9.
v(50-y2)=0.9
Divide each term by v and simplify.
Divide each term in v(50-y2)=0.9 by v.
v(50-y2)v=0.9v
Cancel the common factor of v.
Cancel the common factor.
v(50-y2)v=0.9v
Divide 50-y2 by 1.
50-y2=0.9v
50-y2=0.9v
50-y2=0.9v
Subtract 50 from both sides of the equation.
-y2=0.9v-50
Multiply each term in -y2=0.9v-50 by -1
Multiply each term in -y2=0.9v-50 by -1.
(-y2)⋅-1=0.9v⋅-1+(-50)⋅-1
Multiply (-y2)⋅-1.
Multiply -1 by -1.
1y2=0.9v⋅-1+(-50)⋅-1
Multiply y2 by 1.
y2=0.9v⋅-1+(-50)⋅-1
y2=0.9v⋅-1+(-50)⋅-1
Simplify each term.
Multiply 0.9v⋅-1.
Combine 0.9v and -1.
y2=0.9⋅-1v+(-50)⋅-1
Multiply 0.9 by -1.
y2=-0.9v+(-50)⋅-1
y2=-0.9v+(-50)⋅-1
Move the negative in front of the fraction.
y2=-0.9v+(-50)⋅-1
Multiply -50 by -1.
y2=-0.9v+50
y2=-0.9v+50
y2=-0.9v+50
Take the square root of both sides of the equation to eliminate the exponent on the left side.
y=±-0.9v+50
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
To write 50 as a fraction with a common denominator, multiply by vv.
y=±-0.9v+50vv
Combine the numerators over the common denominator.
y=±-0.9+50vv
Factor 0.1 out of -0.9+50v.
Factor 0.1 out of -0.9.
y=±0.1(-9)+50vv
Factor 0.1 out of 50v.
y=±0.1(-9)+0.1(500v)v
Factor 0.1 out of 0.1(-9)+0.1(500v).
y=±0.1(-9+500v)v
y=±0.1(-9+500v)v
Rewrite 0.1(-9+500v)v as 0.1(-9+500v)v.
y=±0.1(-9+500v)v
Simplify the numerator.
Rewrite 0.1(-9+500v) as (0.562341322)2(-9+500v).
Rewrite 0.1 as 0.316227762.
y=±0.316227762(-9+500v)v
Rewrite 0.31622776 as 0.562341322.
y=±(0.562341322)2(-9+500v)v
y=±(0.562341322)2(-9+500v)v
Pull terms out from under the radical.
y=±0.562341322-9+500vv
Raise 0.56234132 to the power of 2.
y=±0.31622776-9+500vv
y=±0.31622776-9+500vv
Multiply 0.31622776-9+500vv by vv.
y=±0.31622776-9+500vv⋅vv
Combine and simplify the denominator.
Multiply 0.31622776-9+500vv and vv.
y=±0.31622776-9+500vvvv
Raise v to the power of 1.
y=±0.31622776-9+500vvvv
Raise v to the power of 1.
y=±0.31622776-9+500vvvv
Use the power rule aman=am+n to combine exponents.
y=±0.31622776-9+500vvv1+1
y=±0.31622776-9+500vvv2
Rewrite v2 as v.
Use axn=axn to rewrite v as v12.
y=±0.31622776-9+500vv(v12)2
Apply the power rule and multiply exponents, (am)n=amn.
y=±0.31622776-9+500vvv12⋅2
Combine 12 and 2.
y=±0.31622776-9+500vvv22
Cancel the common factor of 2.
Cancel the common factor.
y=±0.31622776-9+500vvv22
Divide 1 by 1.
y=±0.31622776-9+500vvv
y=±0.31622776-9+500vvv
Simplify.
y=±0.31622776-9+500vvv
y=±0.31622776-9+500vvv
y=±0.31622776-9+500vvv
Combine using the product rule for radicals.
y=±0.31622776v(-9+500v)v
y=±0.31622776v(-9+500v)v
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
y=0.31622776v(-9+500v)v
Next, use the negative value of the ± to find the second solution.
y=-0.31622776v(-9+500v)v
The complete solution is the result of both the positive and negative portions of the solution.
y=0.31622776v(-9+500v)v
y=-0.31622776v(-9+500v)v
y=0.31622776v(-9+500v)v
y=-0.31622776v(-9+500v)v
y=0.31622776v(-9+500v)v
y=-0.31622776v(-9+500v)v
Solve for y 0.9=v(50-y^2)

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