Question

The equation x²+18x=27x2+18x=27 has two solutions. The positive solution has the form a−b for positive natural numbers a and b. What is a+b?

a) 27
b) 36
c) 45
d) 46

Answer 1

To find the solution of the quadratic equation x²+18x=27, we rearrange it in the form of ax²+bx+c=0 and solve using the quadratic formula. The positive solution is a - b, which equals -36. Therefore, a + b is closest to 46.

Step-by-step explanation:

To find the solutions of the quadratic equation x²+18x=27, we need to rearrange it in the form of ax²+bx+c=0. In this equation, a=1, b=18, and c=-27. We can then use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values, we get:

x = (-18 ± √(18² - 4(1)(-27))) / (2(1))

Simplifying further, we have:

x = (-18 ± √(324 + 108)) / 2

x = (-18 ± √432) / 2

Now, we can simplify the square root:

x = (-18 ± 20.79) / 2

x = (-18 + 20.79) / 2 or x = (-18 - 20.79) / 2

x = 2.79 / 2 or x = -38.79 / 2

Therefore, the positive solution is equal to a - b = 2.79 - 38.79 = -36. Therefore, a + b = 2.79 + 38.79 = 41.58, which is closest to 46.