Solution of a Quadratic Equation by Completing the Square: A quadratic equation in the form of $$ax^2 + bx + c = 0$$ is a quadratic equation where a, b, and...
Solution of a Quadratic Equation by Completing the Square:
A quadratic equation in the form of is a quadratic equation where a, b, and c are constants. Completing the square is a method used to transform a quadratic equation into a perfect square trinomial, which can be easily solved using the quadratic formula.
Steps to Complete the Square:
Add and subtract the square half of the coefficient of x. This is half the coefficient of x squared.
Divide both sides of the equation by the coefficient of a. This will equal the coefficient of x.
Add and subtract the square root of the constant term to both sides of the equation. This will leave us with the roots of the quadratic equation.
Factor the left side of the equation as a perfect square trinomial. This will give us the solutions to the quadratic equation.
Examples:
Consider the quadratic equation
Following the steps above:
Add and subtract the square half of the coefficient of x, which is 3, to both sides:
Divide both sides by the coefficient of a, which is 1:
Subtract 3 from both sides:
Factor the left side as a perfect square trinomial:
Therefore, the solutions to the quadratic equation are -3 and -3