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
Here's how to solve the first quadratic equation using the formula: The quadratic equation is x^2 + 3x + 1 = 0. The general form of a quadratic equation is ax^2 + bx + c = 0. Comparing the given equation with the general form, we have: a = 1 b = 3 c = 1 The quadratic formula is: x = -b ± sqrt(b^2 - 4ac)2a Step 1: Substitute the values of a, b, and c into the quadratic formula. x = -(3) ± sqrt((3)^2 - 4(1)(1))2(1) Step 2: Simplify the expression under the square root (the discriminant). x = -3 ± sqrt(9 - 4)2 x = -3 ± sqrt(5)2 Step 3: Write out the two solutions. The solutions are: x_1 = -3 + sqrt(5)2 x_2 = -3 - sqrt(5)2 The solutions in surd form are: x = -3 ± sqrt(5)2 That's 2 down. 3 left today — send the next one.