Solve the quadratic equation by completing the square

Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

SIGN UP FOR A FREE TRIAL




The study of algebra consists of solving for the known and unknown variables. There are different kinds of equations in algebra. The quadratic equation is the equation which has the highest degree of the variable as 2. There are different mathematical operations such as addition, subtraction, multiplication, square roots, completing the square and division used to solve the equations according to the requirement.
 
Example 1: Solve the given quadratic equation x2 + 4x +4 = 0; using completing the square method?

Solution: Given equation is x2 + 4x +4 = 0.
Here the unknown variable which needs to be solved for is x.
The degree of the equation is 2(Quadratic equation.)
Completing the square using the formula: (a + b)2 = a2 + 2ab + b2.
This gives x2 + 4x +4 = 0; (x + 2)2 = 0.
Square root on both sides gives x+2 = 0; x =-2

Hence the solution is x = -2

Example 2: Solve the given quadratic equation x2 + 6x +9 = 0; using completing the square method?

Solution: Given equation is x2 + 6x +9 = 0.
Here the unknown variable which needs to be solved for is x.
The degree of the equation is 2(Quadratic equation.)
Completing the square using the formula: (a + b)2 = a2 + 2ab + b2.
This gives x2 + 6x +9 = 0; (x + 3)2 = 0.
Square root on both sides gives x+3 = 0; x =-3.

Hence the solution is x = -3

HAVE A QUESTION? Chat With Our Tutoring Experts Now