Final answer:
This expression is a quadratic equation of the form ax² + bx + c = 0, where the constants are a = 45, b = 27, and c = 18. By substituting these values into the quadratic formula, we find that the equation has no real solutions.
Step-by-step explanation:
This expression is a quadratic equation of the form ax² + bx + c = 0, where the constants are a = 45, b = 27, and c = 18. To complete the statement, we need to find the values of x for which the equation is satisfied:
45ax² + 27ax + 18a = 9a
Simplifying the equation:
45ax² + 27ax + 18a - 9a = 0
45ax² + 27ax + 9a = 0
Dividing the equation by 9a:
5ax² + 3ax + 1 = 0
Now, we have a quadratic equation that we can solve using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values of a = 5, b = 3, and c = 1 into the formula:
x = (-3 ± √(3² - 4(5)(1))) / (2(5))
x = (-3 ± √(9 - 20)) / (10)
x = (-3 ± √(-11)) / (10)
Since the discriminant (b² - 4ac) is negative, the equation has no real solutions. Therefore, the statement cannot be completed with real values of x.