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 quadratic equation 3x^2 + 7x - 15 = 0, we use the quadratic formula: x = -b ± sqrt(b^2 - 4ac)2a In this equation, we have: a = 3 b = 7 c = -15 Step 1: Substitute the values of a, b, and c into the quadratic formula. x = -(7) ± sqrt((7)^2 - 4(3)(-15))2(3) Step 2: Simplify the terms inside the square root and the denominator. x = -7 ± sqrt(49 - (-180))6 x = -7 ± sqrt(49 + 180)6 x = -7 ± sqrt(229)6 Step 3: Calculate the two possible values for x. x_1 = -7 + sqrt(229)6 x_2 = -7 - sqrt(229)6 The exact solutions are: x_1 = -7 + sqrt(229)6 x_2 = -7 - sqrt(229)6 The final answers are x = -7 ± sqrt(229)6.