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
To solve the equation 2x^2 - 4x - 6 = 0 using the quadratic formula, we first identify the coefficients a, b, and c. The general form of a quadratic equation is ax^2 + bx + c = 0. From the given equation, we have: a = 2 b = -4 c = -6 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 = -(-4) ± sqrt((-4)^2 - 4(2)(-6))2(2) Step 2: Simplify the expression under the square root. x = 4 ± sqrt(16 - (-48))4 x = 4 ± sqrt(16 + 48)4 x = 4 ± sqrt(64)4 Step 3: Calculate the square root and simplify further. x = (4 ± 8)/(4) Step 4: Find the two possible values for x. x_1 = (4 + 8)/(4) = (12)/(4) = 3 x_2 = (4 - 8)/(4) = (-4)/(4) = -1 So, the solutions are x=3 or x=-1. Comparing this with the given options: a. x=2 or x=-3 b. x=3 or x=-1 c. x=1 or x=-3 d. x=-2 or x=3 The correct option is b. The final answer is b. x=3 or x=-1. Last free one today — make it count tomorrow, or type /upgrade for unlimited.