# Replace the `GOOGLE_CLOUD_PROJECT` and `GOOGLE_CLOUD_LOCATION` values# with appropriate values for your project.exportGOOGLE_CLOUD_PROJECT=GOOGLE_CLOUD_PROJECTexportGOOGLE_CLOUD_LOCATION=us-central1
exportGOOGLE_GENAI_USE_VERTEXAI=True
fromgoogleimportgenaifromgoogle.genai.typesimportHttpOptionsclient=genai.Client(http_options=HttpOptions(api_version="v1"))response=client.models.generate_content(model="gemini-2.0-flash-thinking-exp-01-21",contents="solve x^2 + 4x + 4 = 0",)print(response.text)# Example response:# To solve the equation x^2 + 4x + 4 = 0, we can use several methods.## **Method 1: Factoring**## We look for two numbers that multiply to 4 (the constant term) and add to 4 (the coefficient of the x term).# These two numbers are 2 and 2 because 2 * 2 = 4 and 2 + 2 = 4.# Therefore, we can factor the quadratic expression as:# (x + 2)(x + 2) = 0# This can also be written as:# (x + 2)^2 = 0## To solve for x, we set the factor (x + 2) equal to zero:# x + 2 = 0# Subtract 2 from both sides:# x = -2## **Method 2: Quadratic Formula**## The quadratic formula for an equation of the form ax^2 + bx + c = 0 is given by:# x = [-b ± sqrt(b^2 - 4ac)] / (2a)## ...### All three methods yield the same solution, x = -2.# This is a repeated root, which is expected since the discriminant (b^2 - 4ac) is 0.## To check our solution, we substitute x = -2 back into the original equation:# (-2)^2 + 4(-2) + 4 = 4 - 8 + 4 = 0# The equation holds true, so our solution is correct.# Final Answer: The final answer is $\boxed{-2}$
