![]() This is the same as factoring out the value of a from all other terms. 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 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.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 you can solve this equation, you will have the solution to all quadratic equations. In a sense then ax 2 + bx + c 0 represents all quadratics. This means that every quadratic equation can be put in this form. The standard form of a quadratic equation is ax 2 + bx + c 0. 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. Solve a quadratic equation by completing the square. 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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