how do you solve x² + 2x = -3 by completing the square?
Answer (1)
Solving x² + 2x = -3 by completing the square will result in x =−1±i√2Move the constant to the other side:x² + 2x = -3Complete the square:Take the coefficient of x (which is 2), divide by 2, and square it: (2 ÷ 2)² = 1Add and subtract 1 on the left-hand side:x² + 2x + 1 - 1 = -3This becomes: (x + 1)² - 1 = -3Isolate the perfect square:(x + 1)² = -3 + 1(x + 1)² = -2Take the square root of both sides:x + 1 = ±√(-2)x + 1 = ±i√2Solve for x:x = -1 ± i√2Therefore, x = -1 + i√2 or x = -1 - i√2 or simply x = -1 ± i√2
