- x^2 + 9x -18
please EXPLAIN step by step like you did the last one
thank you kindly
Sure, I'd be happy to explain step by step how to solve the equation -x^2 + 9x - 18.
Step 1: To solve the equation, we want to find the values of x that make the equation true. To do this, we can use the quadratic formula or try factoring the equation if possible.
Step 2: In this case, the equation does not seem easily factorable, so let's use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = -1, b = 9, and c = -18.
Step 3: Plug in the values of a, b, and c into the formula:
x = (-(9) ± √((9)^2 - 4(-1)(-18))) / (2(-1))
Step 4: Simplify the equation inside the square root:
x = (-(9) ± √(81 - 72)) / (-2)
x = (-(9) ± √9) / (-2)
x = (-(9) ± 3) / (-2)
Step 5: Now, we have two possible solutions:
x = (-(9) + 3) / (-2) => x = -6/2 => x = -3
x = (-(9) - 3) / (-2) => x = -12/2 => x = -6
So the solutions to the equation -x^2 + 9x - 18 are x = -3 and x = -6.