Finite Math Examples

Solve for c ((2c-3)/5)^2+2((2c-3)/5)=8
Step 1
Simplify .
Tap for more steps...
Step 1.1
Simplify each term.
Tap for more steps...
Step 1.1.1
Apply the product rule to .
Step 1.1.2
Raise to the power of .
Step 1.1.3
Combine and .
Step 1.2
To write as a fraction with a common denominator, multiply by .
Step 1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps...
Step 1.3.1
Multiply by .
Step 1.3.2
Multiply by .
Step 1.4
Combine the numerators over the common denominator.
Step 1.5
Simplify the numerator.
Tap for more steps...
Step 1.5.1
Factor out of .
Tap for more steps...
Step 1.5.1.1
Factor out of .
Step 1.5.1.2
Factor out of .
Step 1.5.1.3
Factor out of .
Step 1.5.2
Multiply by .
Step 1.5.3
Add and .
Step 2
Multiply both sides by .
Step 3
Simplify.
Tap for more steps...
Step 3.1
Simplify the left side.
Tap for more steps...
Step 3.1.1
Simplify .
Tap for more steps...
Step 3.1.1.1
Cancel the common factor of .
Tap for more steps...
Step 3.1.1.1.1
Cancel the common factor.
Step 3.1.1.1.2
Rewrite the expression.
Step 3.1.1.2
Expand using the FOIL Method.
Tap for more steps...
Step 3.1.1.2.1
Apply the distributive property.
Step 3.1.1.2.2
Apply the distributive property.
Step 3.1.1.2.3
Apply the distributive property.
Step 3.1.1.3
Simplify and combine like terms.
Tap for more steps...
Step 3.1.1.3.1
Simplify each term.
Tap for more steps...
Step 3.1.1.3.1.1
Rewrite using the commutative property of multiplication.
Step 3.1.1.3.1.2
Multiply by by adding the exponents.
Tap for more steps...
Step 3.1.1.3.1.2.1
Move .
Step 3.1.1.3.1.2.2
Multiply by .
Step 3.1.1.3.1.3
Multiply by .
Step 3.1.1.3.1.4
Multiply by .
Step 3.1.1.3.1.5
Multiply by .
Step 3.1.1.3.1.6
Multiply by .
Step 3.1.1.3.2
Subtract from .
Step 3.2
Simplify the right side.
Tap for more steps...
Step 3.2.1
Multiply by .
Step 4
Solve for .
Tap for more steps...
Step 4.1
Subtract from both sides of the equation.
Step 4.2
Subtract from .
Step 4.3
Factor by grouping.
Tap for more steps...
Step 4.3.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Tap for more steps...
Step 4.3.1.1
Factor out of .
Step 4.3.1.2
Rewrite as plus
Step 4.3.1.3
Apply the distributive property.
Step 4.3.2
Factor out the greatest common factor from each group.
Tap for more steps...
Step 4.3.2.1
Group the first two terms and the last two terms.
Step 4.3.2.2
Factor out the greatest common factor (GCF) from each group.
Step 4.3.3
Factor the polynomial by factoring out the greatest common factor, .
Step 4.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.5
Set equal to and solve for .
Tap for more steps...
Step 4.5.1
Set equal to .
Step 4.5.2
Solve for .
Tap for more steps...
Step 4.5.2.1
Add to both sides of the equation.
Step 4.5.2.2
Divide each term in by and simplify.
Tap for more steps...
Step 4.5.2.2.1
Divide each term in by .
Step 4.5.2.2.2
Simplify the left side.
Tap for more steps...
Step 4.5.2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 4.5.2.2.2.1.1
Cancel the common factor.
Step 4.5.2.2.2.1.2
Divide by .
Step 4.6
Set equal to and solve for .
Tap for more steps...
Step 4.6.1
Set equal to .
Step 4.6.2
Solve for .
Tap for more steps...
Step 4.6.2.1
Subtract from both sides of the equation.
Step 4.6.2.2
Divide each term in by and simplify.
Tap for more steps...
Step 4.6.2.2.1
Divide each term in by .
Step 4.6.2.2.2
Simplify the left side.
Tap for more steps...
Step 4.6.2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 4.6.2.2.2.1.1
Cancel the common factor.
Step 4.6.2.2.2.1.2
Divide by .
Step 4.6.2.2.3
Simplify the right side.
Tap for more steps...
Step 4.6.2.2.3.1
Move the negative in front of the fraction.
Step 4.7
The final solution is all the values that make true.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: