To complete the square of the quadratic function x² + 10x + 4 we need to add 21
Completing The Square
Completing the square is a method in algebra that is used to write a quadratic expression in a way such that it contains the perfect square. In simple words, we can say that completing the square is a process where consider a quadratic equation of the ax² + bx + c = 0 and change it to write it in the form a(x + p)² + q = 0. This method is generally used to find the roots of a quadratic equation.
Completing the square formula is a technique or method to convert a quadratic polynomial or equation into a perfect square with some additional constant. A quadratic expression in variable x: ax² + bx + c, where a, b and c are any real numbers but a ≠ 0, can be converted into a perfect square with some additional constant by using completing the square formula or technique
The equation given is
x² + 10x + 4 = 0
Take 4 to right side
x² + 10x = -4
rewrite in (x + a)² = b form
(x + 5)² = 21
x + 5 = ±√21
x = √21 - 5
x = -√21 - 5
To complete the square, we need to add 21
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