# Solve for b square root of 6-b=2b square root of 6-b

To remove the radical on the left side of the equation, square both sides of the equation.
Simplify each side of the equation.
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify.
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Raise to the power of .
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify.
Apply the distributive property.
Multiply by .
Rewrite using the commutative property of multiplication.
Simplify each term.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Solve for .
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Add to both sides of the equation.
Move to the left side of the equation by subtracting it from both sides.
Factor the left side of the equation.
Reorder terms.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Rewrite as .
Rewrite as .
Factor.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Subtract from both sides of the equation.
Multiply each term in by
Multiply each term in by .
Multiply .
Multiply by .
Multiply by .
Multiply by .
Set the next factor equal to and solve.
Set the next factor equal to .
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
The final solution is all the values that make true.
Exclude the solutions that do not make true.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for b square root of 6-b=2b square root of 6-b

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