To complete the square when a is greater than 1 or less than 1 but not equal to 0, divide both sides of the equation by a. Remember you will have 2 solutions, a positive solution and a negative solution, because you took the square root of the right side of the equation.Ĭompleting the Square when a is Not Equal to 1
Rewrite the perfect square on the left to the form (x + y) 2.Add this result to both sides of the equation.Take the b term, divide it by 2, and then square it.
Move the c term to the right side of the equation by subtracting it from or adding it to both sides of the equation.Your b and c terms may be fractions after this step. If a ≠ 1, divide both sides of your equation by a.First, arrange your equation to the form ax 2 + bx + c = 0.It takes a few steps to complete the square of a quadratic equation. If it is not 1, divide both sides of the equation by the a term and then continue to complete the square as explained below. You can use the complete the square method when it is not possible to solve the equation by factoring.įirst, make sure that the a term is 1.
What is Completing the Square?Ĭompleting the square is a method of solving quadratic equations by changing the left side of the equation so that it is the square of a binomial. The solution shows the work required to solve a quadratic equation for real and complex roots by completing the square.
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