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: Identify the coefficients a, b, and c from the given quadratic equation 2x^2 - 2x + 2 = 0. a = 2 b = -2 c = 2 Step 2: Write down the quadratic formula. x = -b ± sqrt(b^2 - 4ac)2a Step 3: Substitute the values of a, b, and c into the quadratic formula. x = -(-2) ± sqrt((-2)^2 - 4(2)(2))2(2) Step 4: Simplify the expression. x = 2 ± sqrt(4 - 16)4 x = 2 ± sqrt(-12)4 Step 5: Simplify the square root of the negative number. Recall that sqrt(-1) = i. x = 2 ± sqrt(12)i4 x = 2 ± sqrt(4 × 3)i4 x = 2 ± 2sqrt(3)i4 Step 6: Divide all terms by the common factor of 2. x = 2(1 ± sqrt(3)i)4 x = 1 ± sqrt(3)i2 The solutions are: x_1 = 1 + sqrt(3)i2 x_2 = 1 - sqrt(3)i2 The final answers are x = 1 ± sqrt(3)i2. That's 3 down, 1 left today. Send the next one 📸