What is the greatest solution of x in the equation x2+8x−30=18?

Step 1: First, we need to rearrange the equation to make it equal to zero. So, we subtract 18 from both sides of the equation:

x^2 + 8x - 30 - 18 = 0

This simplifies to:

x^2 + 8x - 48 = 0

Step 2: Next, we need to factor the quadratic equation. We are looking for two numbers that multiply to -48 and add to 8. Those numbers are -4 and 12. So, we can rewrite the equation as:

(x - 4)(x + 12) = 0

Step 3: Now, we set each factor equal to zero and solve for x:

x - 4 = 0 => x = 4

x + 12 = 0 => x = -12

Step 4: The solutions to the equation are x = 4 and x = -12. Since the question asks for the greatest solution, the answer is x = 4.