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Solve Quadratic Equations By Completing The Square Method

Solving quadratic equations by completing the square method is important and understanding it helps a lot. Completing the square x+a2=x2+2ax+a2 is the process of rearranging one side of a quadratic equation into a perfect square before solving and is achieved by following these simple rules: 


Simplify the coefficient of x2 to unity by dividing throughout by 2. Using 2x2

completing the square step1

Re-arrange the expression, so that x2 and x terms are on left side of the equal sign (=) and the constant on the right side of the equal sign.

completing the square 2

Half the coefficient of x, where the coefficient of x=5/2

completing the square 3

Then square the result by multiplying the result twice

completing the square 4

Recall the simplified equation and Add the squared result to both sides of the equation 

completing the square 5
completing the square 6

Make a perfect square from the expression and then split the terms into LHS and RHS sides in order to solve for x.

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Evaluate the LHS (Left Hand Side), the expression on the left before the equal sign


Evaluate the RHS (Right Hand Side), the expression on the right after the equal sign


Note: the value of RHS from above is the polynomial determinant D which is equal to 49/16 and greater than zero, suggesting the the solution is real. Combine the two sides LHS and RHS respectively to resolve for roots of x

Area of Triangle Calculator

Note:the plus minus sign (+-) indicates two different answers will be resolved.

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