0.9=v(50-y2)

Rewrite the equation as v(50-y2)=0.9.

v(50-y2)=0.9

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.

(-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

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

Add 1 and 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)