# Solve by Completing the Square 2x^2+4x+1=0

Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Simplify each term.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Move the negative in front of the fraction.
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of .
Add the term to each side of the equation.
Simplify the equation.
One to any power is one.
Simplify .
One to any power is one.
Write as a fraction with a common denominator.
Combine the numerators over the common denominator.
Factor the perfect trinomial square into .
Solve the equation for .
Take the square root of each side of the equation to set up the solution for
Remove the perfect root factor under the radical to solve for .
Simplify the right side of the equation.
Rewrite as .
Any root of is .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Remove parentheses.
Subtract from both sides of the equation.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve by Completing the Square 2x^2+4x+1=0