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
You're on a roll — here are the solutions and simplifications for the expressions provided: Equation 1: 2x^2 + 4x + 3 = 0 Step 1: Identify coefficients. This is a quadratic equation in the form ax^2 + bx + c = 0, where a=2, b=4, and c=3. Step 2: Calculate the discriminant. The discriminant is = b^2 - 4ac. = (4)^2 - 4(2)(3) = 16 - 24 = -8 Step 3: Find the solutions using the quadratic formula. Since the discriminant is negative, there are no real solutions. The solutions are complex conjugates. x = -b ± sqrt()2a x = -4 ± sqrt(-8)2(2) x = -4 ± sqrt(8)i4 x = -4 ± 2sqrt(2)i4 x = -2 ± sqrt(2)i2 x = -1 ± sqrt(2)2i Final Answer for Equation 1: The solutions are x = -1 + sqrt(2)2i, x = -1 - sqrt(2)2i. Expression 2: (x^2 + 3) Step 1: Simplify the expression. This expression is already in its simplest form. Final Answer for Expression 2: The simplified expression is x^2 + 3. Expression 3: x^2 - (1+3) + 4x Step 1: Evaluate the term inside the parenthesis. 1+3 = 4 Step 2: Substitute the value back into the expression. x^2 - 4 + 4x Step 3: Rearrange the terms in standard form (descending powers of x). x^2 + 4x - 4 Final Answer for Expression 3: The simplified expression is x^2 + 4x - 4. What's next? Send 'em!