+1206 The equation \(x^2+18x=27\) has two solutions. The positive solution has the form \(\sqrt{a}-b\) for positive natural numbers a and b. What is \(a+b\)?
+128475 x^2 + 18x = 27 complete the square on x
x^2 + 18x + 81 = 27 + 81
(x + 9)^2 = 108 take both roots
x +9 = √108
x + 9 = √[ 4 * 9 * 3]
x + 9 = √4 *√9 * √3
x + 9 = 2 * 3 * √3
x + 9 = 6√3 subtract 9 from both sides
x = 6√3 - 9
This doesn't have the specified form, Logic....but taking "a" as 3 and "b" as - 9
a + b = 3 + (-9) = -6
