# Solve by Factoring square root of 2x+100- square root of x+1=9

Move to the left side of the equation by subtracting it from both sides.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Add to both sides of the equation.
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.
Apply the distributive property.
Multiply by .
Simplify.
Solve for .
Simplify .
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
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.
Move to the left of .
Multiply by .
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from both sides of the equation.
Subtract from .
Subtract from .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
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.
Solve for .
Simplify .
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply .
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Find the common denominator.
Multiply by .
Combine.
Write as a fraction with denominator .
Multiply by .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Multiply by .
Multiply both sides of the equation by .
Remove parentheses.
Multiply by .
Move to the left side of the equation by subtracting it from both sides.
Combine the opposite terms in .
Subtract from .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
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 .
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
The final solution is all the values that make true.
Solve by Factoring square root of 2x+100- square root of x+1=9