Final answer:
The equation 4x² + 89 = -36x has no real solutions.
Step-by-step explanation:
To solve the equation 4x² + 89 = -36x using the quadratic formula, we rearrange it to the form ax² + bx + c = 0, where a = 4, b = 36, and c = 89:
x² + 9x + 22.25 = 0
Now, we can use the quadratic formula to find the roots of the equation:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula, we have:
x = (-9 ± √(9² - 4(1)(22.25))) / (2(1))
x = (-9 ± √(81 - 89)) / 2
x = (-9 ± √(-8)) / 2
Since the quadratic equation has a negative discriminant (-8), it does not have any real roots. Therefore, the equation has no solution.