(x+5)² + (x-2)² = 37​

Answer:1Step-by-step explanation:To solve the equation (x+5)² + (x-2)² = 37, we can expand the squared terms and simplify the equation:(x+5)² + (x-2)² = 37(x+5)(x+5) + (x-2)(x-2) = 37(x² + 10x + 25) + (x² - 4x + 4) = 37x² + 10x + 25 + x² - 4x + 4 = 372x² + 6x + 29 = 37Now, let's rearrange the equation to set it equal to zero:2x² + 6x + 29 - 37 = 02x² + 6x - 8 = 0Next, let's divide the equation by 2 to simplify it further:x² + 3x - 4 = 0To solve this quadratic equation, we can factor it:(x + 4)(x - 1) = 0Setting each factor equal to zero, we have:x + 4 = 0 or x - 1 = 0Solving for x, we get:x = -4 or x = 1Therefore, the solutions to the equation (x+5)² + (x-2)² = 37 are x = -4 and x = 1.

Answered by Rayverian | 2024-09-04