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 are the solutions for the problems you've worked on: 1) Solve 3x^2 + 4x - 2 = 0 Step 1: Identify the coefficients. For the quadratic equation ax^2 + bx + c = 0, we have a=3, b=4, and c=-2. Step 2: Apply the quadratic formula. The quadratic formula is x = -b ± sqrt(b^2 - 4ac)2a. Substitute the values of a, b, and c: x = -(4) ± sqrt((4)^2 - 4(3)(-2))2(3) Step 3: Simplify the expression. x = -4 ± sqrt(16 - (-24))6 x = -4 ± sqrt(16 + 24)6 x = -4 ± sqrt(40)6 x = -4 ± sqrt(4 × 10)6 x = -4 ± 2sqrt(10)6 Divide all terms by 2: x = -2 ± sqrt(10)3 The solutions are x = -2 ± sqrt(10)3. 2) Solve 2x^2 - 3x - 7 = 0 Step 1: Identify the coefficients. For ax^2 + bx + c = 0, we have a=2, b=-3, and c=-7. Step 2: Apply the quadratic formula. x = -b ± sqrt(b^2 - 4ac)2a Substitute the values: x = -(-3) ± sqrt((-3)^2 - 4(2)(-7))2(2) Step 3: Simplify the expression. x = 3 ± sqrt(9 - (-56))4 x = 3 ± sqrt(9 + 56)4 x = 3 ± sqrt(65)4 The solutions are x = 3 ± sqrt(65)4. 3) Solve 3q^2 - 5q - 5 = 0 Step 1: Identify the coefficients. For aq^2 + bq + c = 0, we have a=3, b=-5, and c=-5. Step 2: Apply the quadratic formula. q = -b ± sqrt(b^2 - 4ac)2a Substitute the values: q = -(-5) ± sqrt((-5)^2 - 4(3)(-5))2(3) Step 3: Simplify the expression. q = 5 ± sqrt(25 - (-60))6 q = 5 ± sqrt(25 + 60)6 q = 5 ± sqrt(85)6 The solutions are q = 5 ± sqrt(85)6. Send me the next one 📸