Finite Math Examples

Solve for x z = square root of 1-x^2+ square root of y^2-1
Step 1
Rewrite the equation as .
Step 2
Solve for .
Tap for more steps...
Step 2.1
Simplify each term.
Tap for more steps...
Step 2.1.1
Rewrite as .
Step 2.1.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2.2
Subtract from both sides of the equation.
Step 3
To remove the radical on the left side of the equation, square both sides of the equation.
Step 4
Simplify each side of the equation.
Tap for more steps...
Step 4.1
Use to rewrite as .
Step 4.2
Simplify the left side.
Tap for more steps...
Step 4.2.1
Simplify .
Tap for more steps...
Step 4.2.1.1
Multiply the exponents in .
Tap for more steps...
Step 4.2.1.1.1
Apply the power rule and multiply exponents, .
Step 4.2.1.1.2
Cancel the common factor of .
Tap for more steps...
Step 4.2.1.1.2.1
Cancel the common factor.
Step 4.2.1.1.2.2
Rewrite the expression.
Step 4.2.1.2
Simplify.
Step 4.3
Simplify the right side.
Tap for more steps...
Step 4.3.1
Simplify .
Tap for more steps...
Step 4.3.1.1
Rewrite as .
Step 4.3.1.2
Expand using the FOIL Method.
Tap for more steps...
Step 4.3.1.2.1
Apply the distributive property.
Step 4.3.1.2.2
Apply the distributive property.
Step 4.3.1.2.3
Apply the distributive property.
Step 4.3.1.3
Simplify and combine like terms.
Tap for more steps...
Step 4.3.1.3.1
Simplify each term.
Tap for more steps...
Step 4.3.1.3.1.1
Multiply by .
Step 4.3.1.3.1.2
Rewrite using the commutative property of multiplication.
Step 4.3.1.3.1.3
Multiply .
Tap for more steps...
Step 4.3.1.3.1.3.1
Multiply by .
Step 4.3.1.3.1.3.2
Multiply by .
Step 4.3.1.3.1.3.3
Raise to the power of .
Step 4.3.1.3.1.3.4
Raise to the power of .
Step 4.3.1.3.1.3.5
Use the power rule to combine exponents.
Step 4.3.1.3.1.3.6
Add and .
Step 4.3.1.3.1.4
Rewrite as .
Tap for more steps...
Step 4.3.1.3.1.4.1
Use to rewrite as .
Step 4.3.1.3.1.4.2
Apply the power rule and multiply exponents, .
Step 4.3.1.3.1.4.3
Combine and .
Step 4.3.1.3.1.4.4
Cancel the common factor of .
Tap for more steps...
Step 4.3.1.3.1.4.4.1
Cancel the common factor.
Step 4.3.1.3.1.4.4.2
Rewrite the expression.
Step 4.3.1.3.1.4.5
Simplify.
Step 4.3.1.3.1.5
Expand using the FOIL Method.
Tap for more steps...
Step 4.3.1.3.1.5.1
Apply the distributive property.
Step 4.3.1.3.1.5.2
Apply the distributive property.
Step 4.3.1.3.1.5.3
Apply the distributive property.
Step 4.3.1.3.1.6
Simplify and combine like terms.
Tap for more steps...
Step 4.3.1.3.1.6.1
Simplify each term.
Tap for more steps...
Step 4.3.1.3.1.6.1.1
Multiply by .
Step 4.3.1.3.1.6.1.2
Move to the left of .
Step 4.3.1.3.1.6.1.3
Rewrite as .
Step 4.3.1.3.1.6.1.4
Multiply by .
Step 4.3.1.3.1.6.1.5
Multiply by .
Step 4.3.1.3.1.6.2
Add and .
Step 4.3.1.3.1.6.3
Add and .
Step 4.3.1.3.2
Reorder the factors of .
Step 4.3.1.3.3
Subtract from .
Step 5
Solve for .
Tap for more steps...
Step 5.1
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 5.1.1
Subtract from both sides of the equation.
Step 5.1.2
Subtract from .
Step 5.2
Divide each term in by and simplify.
Tap for more steps...
Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
Tap for more steps...
Step 5.2.2.1
Dividing two negative values results in a positive value.
Step 5.2.2.2
Divide by .
Step 5.2.3
Simplify the right side.
Tap for more steps...
Step 5.2.3.1
Simplify each term.
Tap for more steps...
Step 5.2.3.1.1
Move the negative one from the denominator of .
Step 5.2.3.1.2
Rewrite as .
Step 5.2.3.1.3
Move the negative one from the denominator of .
Step 5.2.3.1.4
Rewrite as .
Step 5.2.3.1.5
Multiply by .
Step 5.2.3.1.6
Move the negative one from the denominator of .
Step 5.2.3.1.7
Rewrite as .
Step 5.2.3.1.8
Divide by .
Step 5.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5.4
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps...
Step 5.4.1
First, use the positive value of the to find the first solution.
Step 5.4.2
Next, use the negative value of the to find the second solution.
Step 5.4.3
The complete solution is the result of both the positive and negative portions of the solution.