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 of the quadratic equation. The given equation is 3x^2 - 5x - 7 = 0. Comparing this to the standard quadratic form ax^2 + bx + c = 0, we have: a = 3 b = -5 c = -7 Step 2: Write down the quadratic formula. The quadratic formula is: x = -b ± sqrt(b^2 - 4ac)2a Step 3: Substitute the values of a, b, and c into the formula. x = -(-5) ± sqrt((-5)^2 - 4(3)(-7))2(3) Step 4: Simplify the expression. First, simplify the terms: x = 5 ± sqrt(25 - (-84))6 x = 5 ± sqrt(25 + 84)6 x = 5 ± sqrt(109)6 Step 5: Write the two solutions for x. The two solutions are: x_1 = 5 + sqrt(109)6 x_2 = 5 - sqrt(109)6 The final answers are x = 5 ± sqrt(109)6.