Question 1123174
your expression is:


-x^2 - 12x + 1/64


set it equal to y and your equation is:


y = -x^2 - 12x + 1/64


set y equal to 0 and the equation becomes:


0 = -x^2 = 12x + 1/64


add -x^2 - 12x to both sides of the equation to get:


x^2 + 12x = 1/64


take half of the coefficient of the x term and subtract the square of half the coefficint of the x^2 term to form the following equation.


(x+6)^2 - 6^2 = 1/64


add 6^2 to both sides of the equation to get:


(x+6)^2 = 1/64 + 36


simplify to get:


(x+6)^2 = 2305/64


the equation is now in completing the squares form.


take the square root of both sides of this equation to get:


x+6 = sqrt(2305/64)


subtract 6 from both sides to get:


x = sqrt(2305/64) - 6


if that solution is correct, then replacing x with that value in the original equation will make that equation true.


the original equation is -x^2 - 12x + 1/64 = 0


replacing x with sqrt(2305/64) - 6 results in:


-x^2 - 12x + 1/64 = 2.3 * 10^-14.


2.3 * 10^-14 is equal to a decimal point followed by 13 zeros followed by 23.


that looks  like .000000000000023 which is a very small number that you can safely assume would be equal to 0 if the calculator had more internal decimal digits to store.


i did confirm manually that the result is accurate and that replacing x with (sqrt(2305/64) - 6) does indeed lead to -x^2 - 12x + 1/64 = 0.


here's a reference on completing the squares method you might find useful.


<a href = "https://www.purplemath.com/modules/sqrquad.htm" target = "_blank">https://www.purplemath.com/modules/sqrquad.htm</a>