Algebra Examples

Solve by Completing the Square 2x^2+5x-1=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
Cancel the common factor of .
Tap for more steps...
Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
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
Apply the product rule to .
Step 5.1.1.2
Raise to the power of .
Step 5.1.1.3
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
Apply the product rule to .
Step 5.2.1.1.2
Raise to the power of .
Step 5.2.1.1.3
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
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 denominator.
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 7.3
Subtract from both sides of the equation.
Step 8
The result can be shown in multiple forms.
Exact Form:
Decimal Form: