Algebra Examples

Solve by Completing the Square 5x^2-x-4=0
Step 1
Add to both sides of the equation.
Step 2
Divide each term in by and simplify.
Tap for more steps...
Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
Tap for more steps...
Step 2.2.1
Simplify each term.
Tap for more steps...
Step 2.2.1.1
Cancel the common factor of .
Tap for more steps...
Step 2.2.1.1.1
Cancel the common factor.
Step 2.2.1.1.2
Divide by .
Step 2.2.1.2
Move the negative in front of the fraction.
Step 3
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of .
Step 4
Add the term to each side of the equation.
Step 5
Simplify the equation.
Tap for more steps...
Step 5.1
Simplify the left side.
Tap for more steps...
Step 5.1.1
Simplify each term.
Tap for more steps...
Step 5.1.1.1
Use the power rule to distribute the exponent.
Tap for more steps...
Step 5.1.1.1.1
Apply the product rule to .
Step 5.1.1.1.2
Apply the product rule to .
Step 5.1.1.2
Raise to the power of .
Step 5.1.1.3
Multiply by .
Step 5.1.1.4
One to any power is one.
Step 5.1.1.5
Raise to the power of .
Step 5.2
Simplify the right side.
Tap for more steps...
Step 5.2.1
Simplify .
Tap for more steps...
Step 5.2.1.1
Simplify each term.
Tap for more steps...
Step 5.2.1.1.1
Use the power rule to distribute the exponent.
Tap for more steps...
Step 5.2.1.1.1.1
Apply the product rule to .
Step 5.2.1.1.1.2
Apply the product rule to .
Step 5.2.1.1.2
Raise to the power of .
Step 5.2.1.1.3
Multiply by .
Step 5.2.1.1.4
One to any power is one.
Step 5.2.1.1.5
Raise to the power of .
Step 5.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 5.2.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Tap for more steps...
Step 5.2.1.3.1
Multiply by .
Step 5.2.1.3.2
Multiply by .
Step 5.2.1.4
Combine the numerators over the common denominator.
Step 5.2.1.5
Simplify the numerator.
Tap for more steps...
Step 5.2.1.5.1
Multiply by .
Step 5.2.1.5.2
Add and .
Step 6
Factor the perfect trinomial square into .
Step 7
Solve the equation for .
Tap for more steps...
Step 7.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 7.2
Simplify .
Tap for more steps...
Step 7.2.1
Rewrite as .
Step 7.2.2
Simplify the numerator.
Tap for more steps...
Step 7.2.2.1
Rewrite as .
Step 7.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 7.2.3
Simplify the denominator.
Tap for more steps...
Step 7.2.3.1
Rewrite as .
Step 7.2.3.2
Pull terms out from under the radical, assuming positive real numbers.
Step 7.3
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps...
Step 7.3.1
First, use the positive value of the to find the first solution.
Step 7.3.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 7.3.2.1
Add to both sides of the equation.
Step 7.3.2.2
Combine the numerators over the common denominator.
Step 7.3.2.3
Add and .
Step 7.3.2.4
Divide by .
Step 7.3.3
Next, use the negative value of the to find the second solution.
Step 7.3.4
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 7.3.4.1
Add to both sides of the equation.
Step 7.3.4.2
Combine the numerators over the common denominator.
Step 7.3.4.3
Add and .
Step 7.3.4.4
Cancel the common factor of and .
Tap for more steps...
Step 7.3.4.4.1
Factor out of .
Step 7.3.4.4.2
Cancel the common factors.
Tap for more steps...
Step 7.3.4.4.2.1
Factor out of .
Step 7.3.4.4.2.2
Cancel the common factor.
Step 7.3.4.4.2.3
Rewrite the expression.
Step 7.3.4.5
Move the negative in front of the fraction.
Step 7.3.5
The complete solution is the result of both the positive and negative portions of the solution.