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
This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve for X using the quadratic formula: X = -b ± sqrt(b^2 - 4ac)2a From the given equation X^2 + 6X + 1 = 0, we have a=1, b=6, and c=1. Step 1: Substitute the values of a, b, and c into the quadratic formula. X = -6 ± sqrt(6^2 - 4(1)(1))2(1) Step 2: Simplify the expression under the square root. X = -6 ± sqrt(36 - 4)2 X = -6 ± sqrt(32)2 Step 3: Simplify the square root of 32. sqrt(32) = sqrt(16 × 2) = sqrt(16) × sqrt(2) = 4sqrt(2) Step 4: Substitute the simplified square root back into the equation. X = -6 ± 4sqrt(2)2 Step 5: Divide both terms in the numerator by 2. X = -3 ± 2sqrt(2) The two solutions are X = -3 + 2sqrt(2) and X = -3 - 2sqrt(2). X = -3 ± 2sqrt(2) That's 2 down. 3 left today — send the next one.