![]() 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.Let's start with the solution and then review it more closely. Why is that so But hope is not lost We can use a method called completing the square. The square root and factoring methods are not applicable here. Rewrite the perfect square on the left to the form (x + y) 2 If the problem had been an equation of: x2-44x 0 Completing the square would have resulted in x2-44x+484 484 (x-22)2 484 Take square root: x-22 +/- sqrt(484) Simplify: x 22 +/- 22 This results in: x22+22 44 And in x 0 Note: The equation would be easier to solve using factoring. Solving quadratic equations by completing the square Consider the equation x 2 + 6 x 2.So far, we have solved quadratic equations by factoring and using the Square Root Property. Add this result to both sides of the equation If you missed this problem, review Example 7.46.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. ![]()
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