For quadratic equations that cannot be solved by factorising, we use a method which can solve ALL quadratic equations called completing the square.
We use this later when studying circles in plane analytic geometry.
Luckily, we can transform any quadratic equation to the above form.
This transformation is called completing of square.
Need a full solution to a completing the square problem? Ready to take your learning to the next level with “how” and “why” steps?
My Love Is Like A Red Red Rose Essay - Solving Quadratic Equations By Completing The Square Practice Problems
is negative, that above equation has no real roots (square of any real number can't give negative number) Alas, not all quadratic equations are given in the above form.
(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.
(iv) Write the left side as a square and simplify the right side. Find the roots of Step (ii) Rewrite the equation with the constant term (ie. [No need in this example] Step (iii) Complete the square by adding the square of one-half of the coefficient of x to both sides, that is `(b/2)^2`.
But there is a way for me to manipulate the quadratic to put it into that ready-for-square-rooting form, so I can solve.
First, I put the loose number on the other side of the equation: This process creates a quadratic expression that is a perfect square on the left-hand side of the equation.