A quadratic equation is an equation where the highest power of x is x². There are various methods of solving quadratic equations, as shown below.
NOTE: If x² = 36, then x = +6 or -6 (since squaring either of these numbers will give 36). However, Ö36 = + 6 only.
Completing the Square
9 and 25 can be written as 3² and 5² whereas 7 and 11 cannot be written as the square of another exact number. 9 and 25 are called perfect squares. Another example is (9/4) = (3/2)². In a similar way, x² + 2x + 1 = (x + 1)².
To make x² + 6x into a perfect square, we add (6²/4) = 9. The resulting expression, x² + 6x + 9 = (x + 3)² and so is a perfect square. This is known ascompleting the square. To complete the square in this way, we take the number before the x, square it, and divide it by 4. This technique can be used to solve quadratic equations, as demonstrated in the following example.
Solve x² - 6x +…