Can you complete the square with a coefficient

This changes the value of the x -coefficient. Step 4: Complete the square of the expression in parentheses on the left-hand side of the equation. Step 5: Add the result from Step 4 to the parenthetical expression on the left-hand side. Then add a x result to the right-hand side.

To keep the equation true what is done to one side must also be done to the other. When adding the result to the parenthetical expression on the left-hand side the total value added is a x result. So this value must also be added to the right-hand side.

Step 6: Rewrite the left-hand side as a perfect square and simplify the right-hand side. When rewriting in perfect square format the value in the parentheses is the x-coefficient of the parenthetical expression divided by 2 as found in Step 4. Step 7: Divide both sides by a.

Step 8: Take the square root of both sides of the equation. We can complete the square to solve a Quadratic Equation find where it is equal to zero. But a general Quadratic Equation can have a coefficient of a in front of x 2 :. Step 3 Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation.

Step 3 Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation:. Why complete the square when we can just use the Quadratic Formula to solve a Quadratic Equation?

Well, one reason is given above, where the new form not only shows us the vertex, but makes it easier to solve. For example "x" may itself be a function like cos z and rearranging it may open up a path to a better solution. Step 1 Divide all terms by a the coefficient of x 2.