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.
By the way, unless you're told that you to use completing the square, you will probably never use this method in actual practice when solving quadratic equations.
Either some other method (such as factoring) will be obvious and quicker, or else the Quadratic Formula (reviewed next) will be easier to use.
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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.
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.