Question

The equation x^2+12x=73 has two solutions. The positive solution has the form √a-b for positive natural numbers a and b. What is a+b?

Answer 1

Step-by-step explanation:

x^2 + 12x = 73

let's complete the square, the easiest way to solve this particular one

x^2 + 12x + 36 = 73+36

(x + 6)^2 = 109

x + 6 = ± √109

x = -6 ± √109

the positive one looks like

√109 - 6

so a = 1, b = -6

a+b = -5

Answer 2

Answer:

115

Step-by-step explanation:

Like user pReCiOuS4U mentioned,

x^2 + 12x + 36 = 73+36

(x + 6)^2 = 109

x + 6 = ± √109

x = -6 ± √109

This makes a = 109 and b = 6

Since the problem states that it is in the form $\sqrt{a} -b$, b is not negative since you are already subtracting it.

109 + 6 is 115