This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Divide the equation by the coefficient of x^2, which is 2. 2x^2 + 4x + 1 = 0 (2x^2)/(2) + (4x)/(2) + (1)/(2) = (0)/(2) x^2 + 2x + (1)/(2) = 0 Step 2: Move the constant term to the right side of the equation. x^2 + 2x = -(1)/(2) Step 3: Complete the square on the left side. To do this, take half of the coefficient of x (which is 2), square it, and add it to both sides of the equation. Half of the coefficient of x is (2)/(2) = 1. Squaring it gives 1^2 = 1. x^2 + 2x + 1 = -(1)/(2) + 1 Step 4: Factor the left side as a perfect square and simplify the right side. (x+1)^2 = (1)/(2) Step 5: Take the square root of both sides. sqrt((x+1)^2) = ±sqrt((1)/(2)) x+1 = ±(1)/(sqrt(2)) To rationalize the denominator, multiply the numerator and denominator by sqrt(2): x+1 = ±sqrt(2)2 Step 6: Solve for x. x = -1 ± sqrt(2)2 The two solutions are: x_1 = -1 + sqrt(2)2 x_2 = -1 - sqrt(2)2 The solutions can also be written as: x = -2 ± sqrt(2)2 The final answers are x = -1 + sqrt(2)2, x = -1 - sqrt(2)2. Send me the next one 📸