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, where a=3, b=2, and c=6. To simplify or solve this equation, we can use the quadratic formula: x = -b ± sqrt(b^2 - 4ac)2a Step 1: Substitute the values of a, b, and c into the quadratic formula. x = -(2) ± sqrt((2)^2 - 4(3)(6))2(3) Step 2: Simplify the expression under the square root (the discriminant). x = -2 ± sqrt(4 - 72)6 x = -2 ± sqrt(-68)6 Step 3: Simplify the square root of the negative number. We can write sqrt(-68) as sqrt(68)i, where i is the imaginary unit (i = sqrt(-1)). x = -2 ± sqrt(68)i6 Step 4: Simplify sqrt(68). Since 68 = 4 × 17, we have sqrt(68) = sqrt(4 × 17) = 2sqrt(17). x = -2 ± 2sqrt(17)i6 Step 5: Divide both terms in the numerator by the denominator. x = (-2)/(6) ± 2sqrt(17)i6 x = -(1)/(3) ± sqrt(17)3i The solutions are complex numbers. The simplified form of the equation is: x = -(1)/(3) ± sqrt(17)3i