Here is Noah's work: 4x^2-20x+88=0 4x^2-20x=-88 4x^2-20x+25=-88+25 (2x-5)^2=-63 Show how Noah can finish his work using complex numbers.

## Step 1Noah started with the equation . After factoring, he obtained \((2x-5)^2 = -63\).## Step 2To solve this equation for , we need to take the square root of both sides. Since the square root of a negative number is not a real number, we introduce complex numbers.### **Complex numbers are in the form , where is the "real" part of the number and is the "imaginary" part of the number.**## Step 3We can rewrite as .## Step 4Now, we solve for by adding 5 to both sides and then dividing by 2. This gives us two solutions:### **\(x_1 = (5 + \sqrt{-63})/2\)** and ### **\(x_2 = (5 - \sqrt{-63})/2\)**These are the solutions to the equation, and they are complex roots.