# Solve by Completing the Square 3x^2+x-1/2=0

Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply by .
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.
Simplify each term.
Apply the product rule to .
One to any power is one.
Raise to the power of .
Simplify .
Simplify each term.
Apply the product rule to .
One to any power is one.
Raise to the power of .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply by .
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 .
Simplify the denominator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
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 3x^2+x-1/2=0