# 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
fromgoogleimportgenaiclient=genai.Client()response=client.models.generate_content(model="gemini-2.5-pro-exp-03-25",contents="solve x^2 + 4x + 4 = 0",)print(response.text)# Example Response:# Okay, let's solve the quadratic equation x² + 4x + 4 = 0.## There are a few ways to solve this:## **Method 1: Factoring**## 1. **Look for two numbers** that multiply to the constant term (4) and add up to the coefficient of the x term (4).# * The numbers are 2 and 2 (since 2 * 2 = 4 and 2 + 2 = 4).# 2. **Factor the quadratic** using these numbers:# (x + 2)(x + 2) = 0# This can also be written as:# (x + 2)² = 0# 3. **Set the factor equal to zero** and solve for x:# x + 2 = 0# x = -2## This type of solution, where the factor is repeated, is called a repeated root or a root with multiplicity 2.## **Method 2: Using the Quadratic Formula**## The quadratic formula solves for x in any equation of the form ax² + bx + c = 0:# x = [-b ± √(b² - 4ac)] / 2a## 1. **Identify a, b, and c** in the equation x² + 4x + 4 = 0:# * a = 1# * b = 4# * c = 4# 2. **Substitute these values into the formula:**# x = [-4 ± √(4² - 4 * 1 * 4)] / (2 * 1)# 3. **Simplify:**# x = [-4 ± √(16 - 16)] / 2# x = [-4 ± √0] / 2# x = [-4 ± 0] / 2# 4. **Calculate the result:**# x = -4 / 2# x = -2## Both methods give the same solution.## **Answer:**# The solution to the equation x² + 4x + 4 = 0 is **x = -2**.
