The quadratic equation x^{2}-6x=12 is rewritten in the form (x+p)^2=q, where q is a constant. What is the value of p ?

Given the quadratic functions expressed as;

x² - 6x = 12

The value of p given the quadratic expression is -3

Complete the square at the left hand side of the equation.

Add the square of the half of coefficient of x to both sides.

coefficient of x = -6

Half of coefficient of x = -6/2 = -3

Square of the result = (-3)² = 9

Add 9 to both sides of the equation

x² - 6x + 9 = 12 + 9

Factoring the left hand side

(x-3)² = 21

Comparing the result with (x+p)² = q

The value of p wil be -3

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p = - 3

Step-by-step explanation:

Given

x² - 6x = 12

To obtain the required form use the method of completing the square

add ( half the coefficient of the x- term )² to both sides, thus

x² + 2(- 3)x + 9 = 12 + 9

(x - 3)² = 21

Thus p = - 3