Pre-Algebra Examples

Solve for x square root of 3x+28=1+ square root of x+9
Step 1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2
Simplify each side of the equation.
Tap for more steps...
Step 2.1
Use to rewrite as .
Step 2.2
Simplify the left side.
Tap for more steps...
Step 2.2.1
Simplify .
Tap for more steps...
Step 2.2.1.1
Multiply the exponents in .
Tap for more steps...
Step 2.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.2.1.1.2
Cancel the common factor of .
Tap for more steps...
Step 2.2.1.1.2.1
Cancel the common factor.
Step 2.2.1.1.2.2
Rewrite the expression.
Step 2.2.1.2
Simplify.
Step 2.3
Simplify the right side.
Tap for more steps...
Step 2.3.1
Simplify .
Tap for more steps...
Step 2.3.1.1
Rewrite as .
Step 2.3.1.2
Expand using the FOIL Method.
Tap for more steps...
Step 2.3.1.2.1
Apply the distributive property.
Step 2.3.1.2.2
Apply the distributive property.
Step 2.3.1.2.3
Apply the distributive property.
Step 2.3.1.3
Simplify and combine like terms.
Tap for more steps...
Step 2.3.1.3.1
Simplify each term.
Tap for more steps...
Step 2.3.1.3.1.1
Multiply by .
Step 2.3.1.3.1.2
Multiply by .
Step 2.3.1.3.1.3
Multiply by .
Step 2.3.1.3.1.4
Multiply .
Tap for more steps...
Step 2.3.1.3.1.4.1
Raise to the power of .
Step 2.3.1.3.1.4.2
Raise to the power of .
Step 2.3.1.3.1.4.3
Use the power rule to combine exponents.
Step 2.3.1.3.1.4.4
Add and .
Step 2.3.1.3.1.5
Rewrite as .
Tap for more steps...
Step 2.3.1.3.1.5.1
Use to rewrite as .
Step 2.3.1.3.1.5.2
Apply the power rule and multiply exponents, .
Step 2.3.1.3.1.5.3
Combine and .
Step 2.3.1.3.1.5.4
Cancel the common factor of .
Tap for more steps...
Step 2.3.1.3.1.5.4.1
Cancel the common factor.
Step 2.3.1.3.1.5.4.2
Rewrite the expression.
Step 2.3.1.3.1.5.5
Simplify.
Step 2.3.1.3.2
Add and .
Step 2.3.1.3.3
Add and .
Step 3
Solve for .
Tap for more steps...
Step 3.1
Rewrite the equation as .
Step 3.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Subtract from both sides of the equation.
Step 3.2.3
Subtract from .
Step 3.2.4
Subtract from .
Step 4
To remove the radical on the left side of the equation, square both sides of the equation.
Step 5
Simplify each side of the equation.
Tap for more steps...
Step 5.1
Use to rewrite as .
Step 5.2
Simplify the left side.
Tap for more steps...
Step 5.2.1
Simplify .
Tap for more steps...
Step 5.2.1.1
Apply the product rule to .
Step 5.2.1.2
Raise to the power of .
Step 5.2.1.3
Multiply the exponents in .
Tap for more steps...
Step 5.2.1.3.1
Apply the power rule and multiply exponents, .
Step 5.2.1.3.2
Cancel the common factor of .
Tap for more steps...
Step 5.2.1.3.2.1
Cancel the common factor.
Step 5.2.1.3.2.2
Rewrite the expression.
Step 5.2.1.4
Simplify.
Step 5.2.1.5
Apply the distributive property.
Step 5.2.1.6
Multiply by .
Step 5.3
Simplify the right side.
Tap for more steps...
Step 5.3.1
Simplify .
Tap for more steps...
Step 5.3.1.1
Rewrite as .
Step 5.3.1.2
Expand using the FOIL Method.
Tap for more steps...
Step 5.3.1.2.1
Apply the distributive property.
Step 5.3.1.2.2
Apply the distributive property.
Step 5.3.1.2.3
Apply the distributive property.
Step 5.3.1.3
Simplify and combine like terms.
Tap for more steps...
Step 5.3.1.3.1
Simplify each term.
Tap for more steps...
Step 5.3.1.3.1.1
Rewrite using the commutative property of multiplication.
Step 5.3.1.3.1.2
Multiply by by adding the exponents.
Tap for more steps...
Step 5.3.1.3.1.2.1
Move .
Step 5.3.1.3.1.2.2
Multiply by .
Step 5.3.1.3.1.3
Multiply by .
Step 5.3.1.3.1.4
Multiply by .
Step 5.3.1.3.1.5
Multiply by .
Step 5.3.1.3.1.6
Multiply by .
Step 5.3.1.3.2
Add and .
Step 6
Solve for .
Tap for more steps...
Step 6.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 6.2
Move all terms containing to the left side of the equation.
Tap for more steps...
Step 6.2.1
Subtract from both sides of the equation.
Step 6.2.2
Subtract from .
Step 6.3
Subtract from both sides of the equation.
Step 6.4
Subtract from .
Step 6.5
Factor the left side of the equation.
Tap for more steps...
Step 6.5.1
Factor out of .
Tap for more steps...
Step 6.5.1.1
Factor out of .
Step 6.5.1.2
Factor out of .
Step 6.5.1.3
Factor out of .
Step 6.5.1.4
Factor out of .
Step 6.5.1.5
Factor out of .
Step 6.5.2
Factor.
Tap for more steps...
Step 6.5.2.1
Factor using the AC method.
Tap for more steps...
Step 6.5.2.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 6.5.2.1.2
Write the factored form using these integers.
Step 6.5.2.2
Remove unnecessary parentheses.
Step 6.6
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 6.7
Set equal to and solve for .
Tap for more steps...
Step 6.7.1
Set equal to .
Step 6.7.2
Subtract from both sides of the equation.
Step 6.8
Set equal to and solve for .
Tap for more steps...
Step 6.8.1
Set equal to .
Step 6.8.2
Subtract from both sides of the equation.
Step 6.9
The final solution is all the values that make true.