First, let's simplify the expression for Y:
Y = 8x² + 6x + √(-x² - 23x - 90)
Now, let's simplify the square root term:
√(-x² - 23x - 90) = √(-(x² + 23x + 90))
Now, factorize the quadratic term inside the square root:
√(-(x² + 23x + 90)) = √(-1)√((x + 18)(x + 5))
√(-(x² + 23x + 90)) = i√((x + 18)(x + 5))
Now, plug this back into the expression for Y:
Y = 8x² + 6x + i√((x + 18)(x + 5))
So, the simplified expression for Y is:
First, let's simplify the expression for Y:
Y = 8x² + 6x + √(-x² - 23x - 90)
Now, let's simplify the square root term:
√(-x² - 23x - 90) = √(-(x² + 23x + 90))
Now, factorize the quadratic term inside the square root:
√(-(x² + 23x + 90)) = √(-1)√((x + 18)(x + 5))
√(-(x² + 23x + 90)) = i√((x + 18)(x + 5))
Now, plug this back into the expression for Y:
Y = 8x² + 6x + i√((x + 18)(x + 5))
So, the simplified expression for Y is:
Y = 8x² + 6x + i√((x + 18)(x + 5))