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. Step 1: Divide the equation by the number in front of the square term. Example 04: Solve equation 2x2 + 8x - 10 0 by completing the square. 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 This method can be used to solve all types of quadratic equations, although it can be complicated for some types of equations. Isolate x on the left by subtracting or adding the numeric constant on both sides.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.

You see, completing the square is all about making the quadratic equation into a perfect square, engineering it, adding and subtracting from both sides so it becomes a perfect square. In the last video, we saw that these can be pretty straightforward to solve if the left-hand side is a perfect square. Move the c term to the right side of the equation by subtracting it from or adding it to both sides of the equation And I put this big space here for a reason.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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